IN   MEMORIAM 
FLORIAN  CAJORI 


dc 


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Digitized  by  the  Internet  Archive 

in  2007  with  funding  from 

IVIicrosoft  Corporation 


http://www.archive.org/details/elementaryarithmOOhamirich 


ELEMENTARY   ARITHMETIC 

FOR   GRADED   AND   ITNGRADBD 
SCHOOLS,    V-Vr-M-X--  :. 


BY 


SAMUEL   HAMILTON,   Ph.D. 

AUTHOR    OF    "  THE    RECITATION,"    AND    SUPERINTENDENT 
OF   SCHOOLS,   ALLEGHENY   COUNTY,   PA. 


NEW  YORK  .:•  CINCINNATI  •:•  CHICAGO 

AMERICAN    BOOK    COMPANY 


Copyright,  190S,  1909,  by 

SAMUEL   HAMILTON. 

Entered  at  Stationers'  Hall,  London. 


HAM.    ELEM.    AR. 

w.  p.    6 


CAJORf 


(y  n 
2 


/Y^^ 


^^ 


PREFACE 

The  "Elementary  Arithmetic "  is  intended  to  cover  the 
work  of  the  first  five  years.     It  is  divided  into  four  parts. 

Part  One  includes  the  work  ordinarily  done  during  the 
first  and  second  years. 

Part  Two  includes  the  work  of  the  third  year.  It  i& 
devoted  mainly  to  the  presentation  of  the  elementary  facts- 
and  tables  of  arithmetic. 

The  text-book  should  be  placed  in  the  hands  of  the  pupil 
when  he  enters  upon  the  work  found  in  Part  Two. 

Part  Three  covers  the  work  of  the  fourth  year.  Its  pur- 
pose is  to  give  a  mastery  of  the  fundamental  operations,  and^ 
through  the  study  of  problems,  to  develop  the  ability  to  use 
these  operations  in  a  practical  way. 

Part  Four  includes  the  work  of  the  fifth  year.  It  gives 
an  elementary  treatment  of  Fractions,  Decimals,  Percentage,. 
Interest,  Denominate  Numbers,  and  Practical  Measurements.. 

The  aim  of  this  course  is  twofold :  first,  to  give  the  child 
mathematical  skill ;  second,  to  give  him  mathematical  power. 

To  these  ends  attention  is  invited  to  the  following : 

1.  The  prominence  given  to  drill  intended  to  give  skilly 
and  the  frequency  of  systematic  reviews. 

2.  The  Study  of  Problems  intended  to  give  mathematical 
power. 

I     3.    The  plan  which  provides  an  easy  treatment  of  eacli 
subject  before  the  complete  treatment  of  it. 

4.    The  easy  steps  in  gradation. 

5*    The  emphasis  given  to  business  arithmetic. 


iv  PREFACE 

6.  The  appeal  made  to  observation  as  a  stimulus  to  mathe- 
matical thought. 

7.  The  abundance  of  exercises  for  oral  drill. 

The  importance  of  oral  drill  has  led  the  author  to  lay 
special  emphasis  on  this  kind  of  work.  Pupils  should  be 
drilled  thoroughly  on  the  oral  development  and  exercises  in 
each  subject,  before  taking  up  the  written  work. 

In  many  schools  the  unit  of  classification  is  the  half  year. 
With  this  in  view,  the  subject-matter  in  the  third,  fourth,  and 
fifth  years  has  been  separated  into  two  parts.  The  easy  treat- 
ment of  topics  covers  the  first  half  of  the  year,  and  the 
more  complete  treatment  the  second  half. 

SAMUEL   HAMILTON. 


CONTENTS 


PART  I  — FIRST  AND   SECOND  YEARS 


Numbers  to  12 

Liquid  Measures    .     .     .     . 
Halves,  Thirds,  Fourths .     . 

Comparison 

Dry  Measures 

Reading  and  Writing  Num- 
bers to  99 


3-13      Roman  Numbers  to  XX 


6  Addition  .     .     .     .     . 

7  Subtraction  .     .     .     . 

8  Multiplication  by  2     . 
11       Division  by  2     .     .     . 

Inch,  Foot,  and  Yard 


14, 16      Review 


PAGES 

16 

17-20 

21-23 

24,25 

26 

27 

28 


PART  II  — THIRD   YEAR 


First  Half  Year 


Reading  and  Writing  Num- 

bers to  9999     .     .     . 

29,30 

Addition 

31-36 

Subtraction 

37-41 

Addition  and  Subtraction 

42 

Multiplication  by  3  and  4 

43-47 

Practical  Problems     .     . 

48 

Division  by  3  and  4    .     , 

49-53 

Addition  and  Subtraction  o1 

I 

United  States  Money    . 

54,55 

Multiplication  by  5  and  6 

56-59 

Division  by  5  and  6    .     . 

60-62 

Addition       

63 

Subtraction 

64,65 

Multiplication  and  Divisior 

I            66 

Dry  Measures    .... 

67 

Liquid  Measures    .     .     . 

68 

Measures  of  Weight   .     . 

69 

Measures  of  Length    .     . 

70,71 

Secoxd  Half  Year 

Reading  and  Writing  Num- 
bers to  99,999 ;  Roman 

Notation 72 

Addition    and    Subtraction, 

including  Fractions  .     .  73-77 

Review 78 

Multiplication  by  7  and  8    .  79-81 

Division  by  7  and  8    .     .     .  82, 83 
Multiplication      by     Mixed 

Numbers 84 

Multiplication  by  9     .     .     .  85, 86 

Division  by  9 87 

Division  of  U.  S.  Money     .  88 

Review 89,90 

Addition  and  Subtraction    .  91,  92 

Review 93-96 

Comparison 97 

Time  Measures 98,  99 

Surface  Measures  ....  100, 101 

Review 102-106 


CONTENTS 


PART  III  — FOURTH   YEAR 


First  Half  Year 

PAGES 

Reading  and  Writing  Num- 
bers to  999,999,999  .  .  107, 108 
Addition  and  Subtraction  .  109-111 
Multiplication  by  10,  11,  12  112-114 
Division  by  10,  11,  and  12  .  115, 116 
Review  and  Drills  ....  117-120 
Multiplication  Table  ...  121 

Multipliers  ending  in  0  .  .  122, 123 
Divisors  ending  in  0  .  .  .  124, 125 
Multiplication  by  'i"\vo-figure 

Numbers 126,127 

Multiplication    of    Concrete 

Numbers     .....  128,129 

Comparison 130 

Review  of  Short  Division     .  131 

Long  Division  by  Two-figure 

Numbers 132-1.36 

Division  and  Partition    .     .  137 

Review 138-140 

Measures  of  Time  ....  141 

Measures  of  Weight    .     .     .  142 

Measures  of  Length  .  .  .  143, 144 
Measures  of  Surface  .     .     .  144-146 


Second  Half  Year 


Del 


Reading  and  Writing  Num 

bers  to  Billions  .  . 
Review  and  Drills  .  .  . 
Addition  and  Subtraction  of 

Mixed  Numbers  .  . 
Multiplication     by     Three 

figure  Numbers  .  . 
Parts  of  Numbers  ... 
Multiplication     by     Mixed 

Numbers     .     .     . 
Fractional  Parts  of  a 

lar 

Long    Division    by    Three 

figure  Numbers  .  . 
Study  of  Problems  of  Two 

Operations  .     .     . 
Review  of  Division 
Combining  Processes  . 

Analysis 

Comparison  .... 

Bills 

Review  of  Measures    . 
Review     ..... 


147 

148-152 

153-155 


156- 


-158 
159 

160 

161 

162 


163- 


170 
171 
172 
173, 174 
175, 176 
177,178 
179-181 
182-185 


PART  IV  — FIFTH  YEAR 


First  Half  Year 
Fractions 186-235 


Fractional  Equivalents 

Reduction 

Addition 

Subtraction  .... 
Multiplication  .  .  . 
Fractional  Parts      .     . 

Division 

Comparison  .... 
Review  Problems    .    . 


186 
195 
197 
201 
207 
208 
221 
230 
232 


Second  Half  Year 

"* — ^  Decimals 236-253 

Notation  and  Numeration  237 

Comparison  of    Fractions 
and  Decimals ....  239 


Addition 241 

Subtraction 243 

Multiplication     ....  245 

Division 248 

Review  I^roblems    .     .     .  252 

Percentage 254-259 

Interest 258 

Operations      with       United 

States  Money     .     .     .  260,261 

Bills 262-265 

Denominate        Numbers  — 

Tables 266-275 

Practical  Measurements  .     .  276-282 
Lengths  and  Surfaces  .     .  276 

Volume 278 

Surfaces  and  Volumes      .  280 

General  Review     ....  283-288 


ELEMENTARY   ARITHMETIC 

PART   I  — FIRST   AND   SECOND   YEARS 
COUNTING   NUMBERS   TO   TEN 


Count  these  balls.  How  Q^  ^^  ^  (^  <^ 
many  are  there  ?  ^  (^^  ^  ^  ^ 

Count  ten  pupils.  Count  eight  desks.  Count  nine 
books.  Count  the  days  of  the  week.  How  many  are 
there  ? 

Numbers  are  used  to  tell  how  many. 

You  have  named  ten  numbers  and  you  can  write 
them  either  in  words  or  in  figures. 

naught      one      two      three      four      five      six      seven      eight      nine      ten 


0 


1      2 


6 


8        9      10 


FIRST  AND  SECOND  YEAR  [Oral 

THE  NXlMBERS  TWO  AND  THREE 


2=^     Twol's 


3  =  2     Three  Vs 


equals  3. 

2.       1            1 

2 

+  2     +1 

+  1 

©  and  ©  are  ©  0.     ©  ©  and  ©  are  ©  ©  ©. 

1.    1  ball  and  1  ball  are  how  many  balls? 

1  ball  +  1  ball  =  2  balls. 

When  you  unite  2  and  1,  you  add  them  and  the  an- 
swer, 3,  is  called  the  sum. 

The  sign  +  is  read  and  or  plus.  The  sign  =  is 
read   equal   or   equals.      2  +  1  =  3    is    read   2   plus    1 

1  top  2  cups  1  car 

+  2  tops      +  1  cup       +  2  cars 

Sum 

3.  John  had  3  cents  and  lost  one  of  them.  How 
many  cents  had  he  left  ? 

3  cents  —  1  cent  =  2  cents. 

4.  How  many  more  balls  are  3  balls  than  2  balls  ? 
3  balls  less  2  balls  =  1  ball. 

You  have  subtracted  2  balls  from  3  balls.  The  an- 
swer, 1  ball,  is  the  difference  or  remainder. 

The  sign  —  is  read  minus  or  less.  3  —  2  =  1  is  read 
3  minus  2  equals  1. 

5.  Subtract,  beginning  at  the  right: 
3        3        3        2        1 

13        2         11 

Difference  or  remainder 


Oral] 


NUMBERS   TO  TWELVE 


THE   NUMBERS   FOUR   AND   FIVE 


1     2     Four  I's 
3     2     Two  2»s 


5  =  ^    ^     FivePs 


and 


are 


and  ^^^ 


are 


^. 


1.  Draw  flags  to  show  the  following : 

3  flags  +  1  flag  =  ?  5  flags  -  1  flag  =  ? 

3  flags  +  2  flags  =  ?  4  flags  r-  3  flags  =  ? 

2.  Count  the  flags  by  2's.     Two  2's  =  ? 

3.  2  flags  taken  two  times  are flags. 

4.  How  many  times  must  1  flag  be  taken  to  have 

4  flags  ?     4  times  1  flag  = flags. 

5.  2  X  2  flags  = flags. 

The  sign  x  is  read  time  or  times. 
Give  answers,  reading  across  the  page : 


6. 

1x1 

5x1 

1x2 

2x2 

3x1 

7. 

1x3 

1x4 

5x1 

2  +  3 

3  +  1 

8. 

1  +  4 

4-1 

5-2 

4-3 

1  +  4 

9. 
10. 

2x2  rings  = 

1x3  balls  - 

3x1  box 
2x2  boot 

:s  = 

To  THE  Teacher.  —  Practice  on  similar  work  until  pupils  are 
thoroughly  familiar  with  the  combinations  up  to  twelve. 


FIRST  AND  SECOND  YEAE, 


[Oral 


LIQUID  MEASURES 


For  this  exercise 
a  set  of  liquid  meas- 
ures should  bemused. 

1.  Fill  the  pint 
measure  with  water 
and  empty  it  into 
the  quart  measure. 
Do  this  a  second 
time.  You  have 
shown  that  2  pints  equal  a  quart. 

2.  A  quart  is  how  many  times  a  pint?     A  pint   is 
what  part  of  a  quart  ? 

3.  Show  by  mea^ring  with  the  quart  measure  that 
4  quarts  equal  a  gallon. 

4.  A  gallon  is  how  many  times  a  quart  ?     A  quart  is 
what  part  of  a  gallon  ? 

5.  How  many  times  can  the  teacher  fill  Mary's  half- 
pint  milk  bottle  from  the  pint  measure  ? 

6.  Clare  gets  a  pint  of  milk  each  morning  and  even- 
ing.    How  many  pints  does  he  get  in  two  days  ? 

7.  Clare  pays  2  cents  for  a  pint  of  milk.     How  much 
does  he  pay  for  2  pints  ? 

8.  Raymond  delivers,  each  day,  4  quart  bottles  of 
milk.     How  many  gallons  does  he  deliver? 

9.  Henry  goes  to  the  store  for  2  quarts  of  molasses. 
How  many  pints  does  he  get  ? 


Oral] 


NUMBERS   TO   TWELVE 


HALVES,   THIRDS,   AND  FOURTHS 

1.  Cutan  apple  into 
2  equal  parts.  What 
is  one  part  called  ? 

2.  Into  how  many 
halves  can  an  apple  be  cut  ?    an  orange  ?    a  pie  ? 

One  half  of  1  is  written  |. 

3.  I  of  2  oranges  =  —  orange ;  ^  of  4  oranges  = 
—  oranges. 

4.  Cut  an  apple  into  3 
equal  parts.  What  is  1  part 
called? 

One  third  of  1  is  written  I. 

5.  ^  of  3  pennies  =  ?  i  of 
4  splints  =  ? 

6.  Cut  an  apple  into  4  equal 
parts.  Each  part  is  named  one 
fourth,  or  one  quarter. 

One  fourth  of  1  is  written  |. 

7.  How  many  fourths  of  an  apple  make  a  whole 
apple  ? 

8.  Write  in  figures :  one  half ;  one  third  ;  one  fourth. 

9.  Find  ^  of  4  cents ;  ^  of  3  cents ;  |^  of  2  cents. 

10.  Find  1  of  4 ;  1  of  3  ;  i  of  2  ;  i  of  1 ;  i  of  4. 

11.  Draw  a  circle  showing  halves;  another  showing 
thirds  ;  one  showing  fourths. 


FIRST   AND   SECOND   YEAR 


[Oral 


COMPARISON 
1.   Which  line  is  the  shortest  ?  the  longest  ? 


2.  Which  lines  are  shorter  than  c  ? 

3.  Which  line  is  one  half  as  long  as  6  ? 

4.  Which  line  is  one  fourth 
as  long  as  6^  ? 

5.  ^  is  how  many  times  as 
large  as  (7? 

6.  How    many   times   larger 
than  (7  is  ^  ? 

7.  Are  A,  B,  and  C  of  the 


A 

B 

C 

Oblong 

same  width  ?    How  many  square 
corners  has  each  one  ? 

8.  How  many  sides  of  A  have 
the  same  length  ? 

9.  How  many  oblongs  are  there  in  ^  ? 

10.  How  many  equal  sides  has  this 
figure  ?  how  many  square  corners  ? 

11.  What  is  the  name  of  the  figure? 
How  long  is  each  side  ? 

12.  How  many  inches  is  it  around 
the  square  ? 

13.  One  inch  is  what  part  of  two  inches  ? 

14.  Two  inches  are  what  part  of  4  inches  ? 


One 
Square  Inch 

1  sq.  in. 


Oral]  NUMBERS   TO   TWELVE 

THE   NUMBERS   SIX   AND   SEVEN 


6  = 


3      Six  Ps 

Three  2»s 
3      Two  3»s 


7  = 


1     2    3 
6    5    4 


Seven  l*s 


1.    With  convenient  objects  show  these  combinations  : 
5  marbles  + 1  marble  =  ?  7  marbles  —  4  marbles  =  ? 

4  marbles  +  3  marbles  =  ?  6  marbles  —  1  marble  =  ? 

2  marbles  4-  4  marbles  =  ?  7  marbles  —  3  marbles  =  ? 


2.    Add: 

2        2 
4        5 


3.    Fill  in  the  blank  spaces  and  add : 

()  ( )  ()  ()  ( )  ( )  ()  ()  ()  () 

5243332161 


6       5 

7 

6 

5 

4 

7 

6 

6 

5 

4.   Subtract: 

7        6 
6       5 

6 
3 

6 
1 

7 
5^ 

7 
2 

7 
4 

6 
2 

6 

4 

7 
3 

5.  Place  six  marbles  in  two  equal  groups ;  in  three 

equal  groups. 

6.  Give  answers  at  sight : 
3x2  2x3 

1  of  6  i  of  3 

-    2  +  2  +  2  =  ?  3  +  3  =  ? 

3  +  2  +  1  =  ?  linG,- 


7x1 


7-4 


iof4 

|of  6 

1+3+2=? 

times  ? 

3+2+2=? 

10 


FIRST   AND   SECOND   YEAR 


[Oral 


THE   NUMBERS   EIGHT   AND   NINE 


,     o    Q    4      Eight  I's 

8  =  ^     ^    ^    ^      Four   2>s 

7     6    5    4      Two    4»s 

9^1     2    3    4      Nine    Vs 
8    7    6    5      Three  3»s 

1.  With  objects  show  the  combinations  that  make 
8  ;  that  make  9. 

2.  Count  to  8  by  2's.            ?x2  =  8?          ?x4  =  8? 

3.  Count  to  9  by  3's.            ?x3  =  9?          ?x2  =  6? 
Add  up,  then  down  : 

4.  432723456 
456176543 

5.   3422130234 
2353302621 
3113456144 

6.  From  9  take  8 ;  take  7;6;5;3;2;4;1;9. 

7.  Subtract : 
8868878888 
3731654852 

8.  In  8  blocks,  how  many  groups  of  2's  are  there  ? 
In  9,  how  many  groups  of  3's  are  there  ? 

1  time    2  =  ? 

3  times  3  =  ?      2  is  contained  in  4, times. 

3  times  2  =  ?      3  is  contained  in  6, times. 

4x2  =  ?  2  is  contained  in  8, times. 

9.'4  +  4  =  ?         5  +  4  =  ?         8h-4  =  ?         iof8  =  ? 


10.    iof6  =  ? 


Jof  6  =  ? 


iof9  =  ? 


Jof  8  =  ? 


Oral] 


NUMBERS   TO   TWELVE 


11 


DRY  MEASURES 


Pint         Quart  Peck  Bushel 

1.  Name  articles  that  you  can  purchase  by  the  peck 
or  by  the  bushel. 

2.  Why  are  these  measures  called  "  dry  measures  "  ? 

3.  The  smallest  dry  measure  shown  in  the  picture 
is  called  a  pint.  Fill  a  pint  measure  with  sand  and 
empty  it  into  the  quart  measure.  Do  this  again.  Is 
the  quart  measure  now  full  ?  You  have  shown  that 
2  pints  equal  a  quart. 

4.  What  part  of  a  quart  is  a  pint  ? 

5.  Show  by  measurement,  as  in  example  3,  that 
8  quarts  equal  a  peck.     A  quart  is  what  part  of  a  peck  ? 

6.  Show  as  before  that  4  pecks  equal  a  bushel.  A 
peck  is  what  part  of  a  bushel  ? 

7.  A  bushel  is  how  many  times  a  peck  ?  A  peck  is 
how  many  times  a  quart  ? 

8.  Subtract: 

8  qt.  7  qt.  8  pk.  6  pt.  8  bu. 

4  qt.  *  3  qt.  3  pk.  4  pt.  5  bu. 


12 


FIRST   AND   SECOND   YEAR 


[Oral 


THE   NUMBERS   TEN   AND   ELEVEN 


10  =  ^     -i    d    4    D     Pi      2's 
9    8     7    6    5     !,       1 
Two  5*s 


11 


12  3  4  5 
10  9  8  7  6 


Eleven  1' 


Illustrate  the  combinations  with  convenient  objects 
or  drawings. 


1.   Add  up,  then  down : 

10       2       0       1 

1 

4 

3 

2 

4 

2       4       3       3       9 

6 

5 

1 

5 

7 

8       6      5       7       1 

4 

2 

6 

2 

0 

2.  From  10  take  3  ;  take  5  ;  7  ;  8  ;  4 ;  2  ;  9. 

3.  .Give  missing  numbers  : 


2x  5, +  ?=11 
11-9  =  ? 
11-4  =  ? 


4  +  4  +  ?=  11       3  +  3  +  3+?  =  11 

5  +  5  +  ?=  11       5x2, +  ?=11 

6  +  3  +  ?=  11       6x1,  +  ?=  11 

4.  Name  the  piece  of  mone}^  that  has  the  same  value 
as  ten  pennies.     10  cents  equal  one  dime. 

5.  How  many  nickels  equal  1  dime  ? 

6.  5  dollars  +  3  dollars  +  ?  =  11  dollars. 

The  sign  $  may  be  used  for  the  word  dollar  or  dollars, 
and  the  sign  ^  indicates  cent  or  cents.  $  8  +  $  3  =  ? 
$5  +  $6  =  ?     $9  +  82=?     4^  +  7^  =  ?     10^+1^=? 

7.  In  11,  there  are 4's  and over. 

In  11,  there  are 5's  and over. 


In  11,  there  are 


3's  and 


over. 


Oral] 


NUMBERS   TO  TWELVE 


THE   NUMBER  TWELVE 


lb 


1.  Draw  12  lines.  Erase  J  of 
them.    What  is  i  of  12  ? 

2.  Count  the  eggs  that  you 
see  in  the  basket. 


3.    What  name  is  sometimes 
given  to  12  eggs  ?    to  12  pins  ? 
to  12  lemons  ? 
12  things  equal  one  dozen. 
4.    How  many  oranges  equal  ^  of  a  dozen  ? 
6.   What  number  is  doubled  to  make  12  ? 


6.    Make  problems  with  : 
4x3  cents  3x4  apples 

6x2  horses  5x2  dollars 

1  of  12  peaches 

Subtract  at  sight : 


1  of  12  cars 


2x6  games 
2x4  cakes 
J  of  12  apples 


r 


7.  12 

12 

12 

12 

12 

12 

12 

12 

3 

4 

5 

6 

7 

8 

9 

2 

8.  10 

10 

10 

10 

10 

10 

10 

10 

2 

3 

4 

5 

6 

7 

8 

9 

tn 

11 

11 

11 

11 

11 

11 

11 

3 

4 

5 

6 

7 

8 

9 

2 

xo.    Make  problems  with  the  above  numbers. 


14 


FIRST  AND  SECOND  YEAR    [Oral  and  Written 


WRITING  AND  READING  NUMBERS 

1.  Count  thirteen,  written  13. 

2.  Count  fourteen,  written  14. 

3.  Count  fifteen,  written  15. 

4.  Write  sixteen,  seventeen,  eighteen,  nineteen. 

The  figure  0  is  called  naught,  or  zero.  It  stands  for 
nothing.  When  placed  to  the  right  of  1,  the  figures 
stand  for  teii ;  when  placed  to  the  right  of  2,  the  figures 
stand  for  tiventy. 

5.  Count  twenty-one,  written  21 ;  twenty-two,  writ- 
ten 22  ;  twenty-five,  written  25. 

6.  Write  twenty-six,  twenty -seven. 

7.  Count  thirty,  written  30;  forty,  40;  fifty,  50; 
sixty,  60 ;  seventy,  70 ;  eighty,  80  ;  ninety,  90. 

Count  ninety-nine,  written  99. 

8.  Make     a     number 


board  and  write  numbers 
to  99  thus  : 

The    first    column   is 
made     up    of    the    ten 

digits. 

9.    Write  in  figures  : 
Twenty-five,  thirty-five, 
forty-three,         seventy- 
three,  sixty-four,  eighty- 
four,  fifty-five,  seventy-six. 

Twenty-five  cents. 

Forty-five  cents. 


10  20 
1121 


12  2'j 


13  23 
14124 
I5I25 
1626 


17 

18 
19 


27 
28 
29 


30 
31 


32 


33 


34 
35 
36 
37 

38 
39 


40 
41 
42 


50 
51 


52162 


435363 
54:64 
55J65 

46156  66 


44 
45 


57 

58 
59 


67 
68 
69 


70 
71 


72 


80 
81 

82 


83 


90 
91 

92 


93 


76 

77 


8494 
85|95 
86  96 


87 


88 


89 


97 
98 
99 


Sixty  dollars. 
Seventy-one  dollars. 


Oral] 

ADDITION 

IIP    1.   Head: 
14        24 

55 

READING   NUM] 

48        51 

15        34 

56 

49        56 

16        44 

57 

■  50        59 

15 


64 

70 

91 

40 

60 

80 

90 

55 

76 

89 

99 

73 

The  right-hand  figure  in  a  number  is  called  ones' 
figure ;  the  second  figure  is  called  tens'  figure. 

Point  out  the  ones  and  the  tens  in  each  of  the  above 
numbers;  thus,  14  is  1  ten  and  4  ones. 

Table  of  Combinations  in  Addition 

In  addition  there  are  45  different  combinations  of 
figures,  taken  two  at  a  time,  and  17  different  sums  or 
amounts.      Use  these  combinations  for  drill  frequently  : 


1 

2 

2     3               3 

4 

3 

4 

5 

1 

1 

2     1               2 

1 

3 

2 

1 

4 

5 

6 

4     5     6     7 

5 

6 

7 

8 

3 

2 

1 

i.  1  1  1 

4 

3 

2 

1 

5 

6 

7     8 

9 

6 

7 

8 

9 

5 

4 

3     2 

1 

5 

4 

3 

2 

6 

7 

8     9 

7     8    9 

7 

8 

9 

6 

5 

4     3 

6     5^    4 

7 

6 

8 

9 

8     9 

9 

9 

7 

6 

8     7 

8 

9 

16 


FIRST   AND   SECOND   YEAR 


[Written 


4 

5 

6 

IV 

V 

VI 

10 

11 

12 

X 

XI 

XII 

ROMAN   NUMBERS   TO   TWENTY 

1.  The  Romans  wrote  all  numbers 
up  to  49  with  the  use  of  three  let- 
ters, I,  Y,  X.  I  stands  f or  1 ;  V 
stands  for  5;    X  stands  for  10. 

2.  This  is  how  the  Romans  wrote 
their  first  twelve  numbers : 

1  2  3 

I  II  III 

7  8  9 

VII  VIII  IX 

3.  Write    the    first    twelve    Roman    numbers    from 
memory. 

4.  Read   the    Roman    numbers   on   the   clock   face. 
On  clock  faces  IIII  is  used  for  IV. 

5.  Copy  the  following  numbers  : 
.  13        14         15         16         17 
XIII     XIV      XV      XVI     XVII 

6.  Write  in  Roman  numbers,  9. 
in  the  letters  will  make  11. 

7.  Write  the  Roman  numbers  from  1  to  20. 

8.  What  time  is  it  by  the  clock  in  the  picture  ? 

The  short  hand  is  called  the  hour  hand.     The  long 
hand  is  called  the  minute  hand. 

9.  Show  the  position  of  the  hands   at  30  minutes 
after  9  ;  at  30  minutes  after  10  ;  at  30  minutes  after  11. 


18  1^        20 

XVIII    XIX     XX 

Show  what  change 


Oral  and  Written]  ADDITION  17 

t  ADDITION 

Sti 


State  sums  at  sight : 

ah  c         d         ^         f         9         7i        i         j 

22       2       2222222 

76      82      7462504153643072 

2.  Change  the  2  above  to  3  and  add ;  then  to  4 : 

3.  2222222222 
85      65     75     55     45     63      73     93     43     83 


4.  3333444444 

59496979     4938     48      8878     5_8 

5.  2324625252 
42  0  3232435 
3^43       1041^103 

6.  A  boy  spent  25  cents  for  a  book  and  12  cents 
for  a  slate.     How  much  did  he  spend  for  both? 

Write  ones  under  ones  and  tens  under 
25  cents       tens.      Add    the  right-hand  column  and 
12  cents       place  the  total,  7,  underneath.     Add  the 
37  cents       second  column  and  write  the  total   un- 
derneath.   The  answer  is  37  cents. 

IB      7.    Find  the  sum  of : 

25  apples  and  63  apples  24  boys  and  15  boys 

37  cakes  and  42  cakes  32  chairs  and  26  chairs 

81  lemons  and  17  lemons  47  books  and  22  books 

42  balls  and  24  balls  36  bats  and  52  bats 


18  FIRST   AND   SECOND   YEAR  [Written 


Add: 

a 

h 

c 

d 

e 

/ 

9 

1.      20 

30 

40 

50 

60 

30 

50 

30 

10 

10 

20 

10 

40 

30 

2. 


3. 


31 

21 

23 

32 

12 

30 

69 

12 

32 

13 

23 

33 

13 

20 

42 

44 

44 

43 

14 

33 

82 

21 

23 

24 

34 

44 

23 

14 

Add  upward  ;  test  by  adding  downward  : 

4.    $45       $25       $35    •  $34      $42       $55      $44 

$14       $33       $54       $35       $45       $33      $22 


5. 


S16 

$45 

$67 

$72 

$81 

$83 

$59 

S31 

$54 

$21 

$25 

$12 

$15 

$20 

Only  things  having  like  names  can  be  added. 

a  b  c  d  e 

6.    17  boys        36  caps        56  balls         35^  46  ft. 

12  boys        21  caps         32  balls         24^  22  ft. 


7. 


a 
12  girls 
10  girls 
23  girls 

b 
34  men 
22.  men 
41  men 

c 
14  tops 
13  tops 
21  tops 

d 
15  books 
20  books 
31  books 

14  cars 
32  cars 
22  cars 

12  boxes 
43  boxes 
31  boxes 

26  hats 
42  hats 
31  hats 

16  days 
22  days 
41  days 

Written] 


ADDITION 


19 


I 


ADDITION 

1.    There  are  54  houses  on  one  street  and  28  on  an- 
other.    How  many  are  there  on  both  streets  ? 
(  Write  ones  under  ones  and  tens  under 

54  houses       tens.     Add  the  ones'  column.     The  sum 
28  houses       is  12  ones,  or  1  ten  and  2  ones.     Write 
82  houses       the  2  under  the  ones'  column  and  add 
f  the  1  ten  to  the  tens'  column.     1  ten  +  2 

^ens  +  5  tens  =  8  tens.     The  answer  is  82  houses. 


I 


Add  and  test : 
a  b 

2.  36  47 
25    24 


c  d 

42    54 
39    36 


« 

48 
34 


35 

27 


64 

28 


3.  46 

19 

29 

18 

38 

17 

39 

36 

24 

10 

36 

17 

46 

45 

4.  19 

21 

32 

23 

31 

42 

13 

14 

19 

4 

15 

43 

16 

46 

3 

12 

16 

6 

8 

17 

18 

5.  11 

16 

19 

41 

39 

42 

15 

31 

10 

20 

23 

20 

18 

41 

29 

49 

17 

18 

18 

20 

38 

6.  30 

40 

32 

9 

8 

15 

13 

17 

19 

30 

14 

20 

20 

68 

28 

34 

9 

16 

9 

38 

14 

7.   Count  by  3's  to  36  ;  to  75.     By  4's  to  88. 


20  FIRST  AND   SECOND   YEAR  [Written 

ADDITION 

1.  Thomas  has  $24  in  the  bank  and  $17  in  his 
pocket.     How  many  dollars  has  he  ? 

2.  A  farmer  sold  26  bushels  of  apples  on  Monday, 
35  bushels  on  Tuesday,  and  30  bushels  on  Wednesday. 
How  many  bushels  did  he  sell  in  the  three  days  ? 

3.  On  Tuesday  a  newsboy  sold  28  morning  papers 
and  44  evening  papers.     How  many  papers  did  he  sell  ? 

4.  A  girl  had  42  cents  left  after  spending  25  cents 
for  ribbon  and  10  cents  for  pins.  How  much  money 
had  she  at  first  ? 

5.  Mrs.  Jackson  spent  $24  for  a  suit,  $31  for  a  coat, 
and  $12  for  a  hat.     How  much  did  all  cost  ? 

6.  Fred  planted  29  potatoes  in  one  row,  31  in  an- 
other, and  33  in  a  third  row.  How  many  potatoes  did 
he  plant  all  together  ? 

7.  Ned  spent  35^  for  a  ball,  25^  for  a  bat,  and  10/ 
for  car  fare.     How  much  did  he  spend  ? 

8.  The  girls  spent  at  the  park,  1 5  /  for  ice  cream, 
20/  on  the  roller  coaster,  35/  in  the  picture  gallery, 
and  12/  for  popcorn.  How  much  did  they  spend  for 
all? 

9.  It  took  Mary  16  minutes  to  sweep  and  dust  the 
library,  12  minutes  for  the  dining  room,  and  21  minutes 
for  the  parlor.    How  long  did  it  take  for  the  three  rooms  ? 

10.   Edwin  has  43  marbles,  and  Walter  has  24  more 
than  Edwin.     How  many  marbles  has  Walter  ? 


Oral]  SUBTRACTION  21 

B  SUBTRACTION 

^     1.    Mary  has    9    cents.     She  spends   5    cents.     How 
many  cents  has  she  left  ? 

2.  A  farmer  had  7  cows.  After  selling  a  number  he 
had  4  left.     How  many  did  he  sell  ? 

IB     ^'    ^^^^    ^^^    1^    towels   to  iron.     When   she   had 
ironed  9,  how  many  were  left  to  iron  ? 

IB     4.    Liicy  had  12  roses  and  gave  Mary  5  roses.     How 
'many  roses  had  Lucy  left  ? 

Table  of  Combinations  in  Subtraction 

In  subtraction  there  are  45  different  combinations  of 
figures,  taken  two  at  a  time.  Use  these  combinations 
for  drill  frequently : 


9 

9 

9 

9 

9 

9 

9 

9 

9 

1 

2 

3 

4 

5 

6 

7 

8 

9 

8 

8 

8 

8 

8 

8 

8 

8 

rr 
i 

1 

2 

3 

4 

5 

6 

7 

8 

1 

7 

7 

7 

7 

7 

7 

6 

6 

6 

2 

3 

4 

5 

6 

7 

1 

2 

3 

G 

6 

6 

5 

5 

5 

5 

5 

4 

4 

5 

6 

1 

2 

3 

4 

5 

1 

4 

4 

4 

3 

3 

3 

2 

2 

1 

1     "* 

3 

4 

1 

2 

3 

1 

2 

1 

1     — 
1 

~ 

— 

~ 

~ 

22 


FIRST   AND   SECOND   YEAR 


[Writtea 


SUBTRACTION 

1.  James  had  48  cents.     He  spent  25  cents.     How 

many  cents  had   he   then  ? 
48  cents  Write  ones  under  ones  and  tens  under 

25  cents       tens,    8  ones  —  5  ones  =  3  ones.     Write  the 
23  cents       three  ones  in  ones'  place.    4  tens  —  2  tens  = 

2  tens.     The  answer  is  23  cents. 

Test—  23  +  25  =  48. 
Only  like  numbers  can  be  subtracted. 
Subtract  and  test : 

a  b  c  d  e 

2.  44  38  56  64  49 
22          13          13          21          23 


/ 

ff 

65 

45 

32 

23 

3.  58 

65 

68 

57 

69 

86 

77 

33 

41 

15 

24 

34 

42 

33 

4.  77 

88 

75 

96 

87 

94 

52 

44 

55 

25 

46 

53 

41 

40 

5.  67 

59 

88 

97 

76 

85 

34 

52 

45 

56 

27 

86 

64 

30 

6.  99 

96 

87 

79 

98 

77 

59 

38 

74 

64 

38 

84 

63 

50 

7.  89 

94 

59 

97 

99 

89 

74 

19 

91 

18 

82 

29 

78 

24 

8.   Make  and  solve  50  examples  like  the  above. 


Written]  PRACTICAL  PROBLEMS  23 


k 


PRACTICAL   PROBLEMS 

1.  David  is  1 4  years  old  and  Walter  is  7  years  younger. 
How  old  is  Walter  ? 

•       2.  Edna  spent  35  cents  for  butter.    She  gave  the  clerk 
a  half-dollar.     How  much  change  should  she  receive  ? 

3.  A  postal  clerk  sold  43  postal  cards  one  week, 
and  67  the  next  week.  How  many  more  did  he  sell  in 
the  second  week  than  in  the  first  week  ? 

4.  A  man  lives  68  miles  from  the  city  and  has  trav- 
eled 24  miles  toward  the  city.  How  many  miles  has  he 
yet  to  travel  ? 

5.  Tom  drove  home  78  cows  and  Ned  56.  How 
many  more  cows  were  there  in  Tom's  herd  than  in  Ned's? 

6.  Edna  had  78  pieces  in  her  doll's  dinner  set,  but  36 
plates  were  broken.     How  many  pieces  remained  ? 

7.  Mr.  Wilson's  farm  contains  76  acres  of  land,  which 
is  14  acres  more  than  his  brother's  farm  contains.  How 
many  acres  are  there  in  his  brother's  farm  ? 

8.  William  rode  27  miles  on  his  bicycle  on  Thursday 
and  14  miles  on  Friday.  How  much  farther  did  he  ride 
the  first  day  than  the  second  ? 

9.  Make  problems  with : 

pupils  $  pictures  lamps  books 

46-14         37-24         63-12         48-36         73-21 
66-43         62-31         84-21         46-24         36-15 

10.    34  children  were  invited  to  Kate's  party.     How 
many  of  them  were  absent,  if  only  22  of  them  attended? 


24 


FIRST   AND   SECOND   YEAR 


[Oral 


He  could 


MULTIPLICATION 

1.  What  is  the  cost  of  two  2-cent  pencils?    2x2^=? 

2.  How  much  should  you  pay  for  three  2-cent  apples  ? 
four  2-cent  tops  ?  five  2-cent  stamps  ?  six  2-cent  papers  ? 

3.  James  counted  2^  seven  times;  thus,  2^  +  2^  +  2^-1- 
2^  +  2^  +  2^  +  2^,  and  found  that  he  had  14^. 
have  said  seven  2's  are  14,  or  7  x  2  =  14. 

4.  Write  in  two  other  forms :  8x2  =  16; 
nine  2's  =  18;  10x2  =  20. 

5.  Build  the  table  of  2's  thus : 
Write   the   sum   of   each  column  2 

beneath  it.     Look  at  each   column.        2    2 

See  how  many  2's  it  contains.     Say, 

1x2  =  2;  2x2  =  4;  3x2  =  6;  4x2  =  8;  5x2  =  10; 

6x2  =  12;  etc. 

6.  Find  products : 

5x2  caps         8x2  plums         9x2  birds        4x2  cups 
6x2  dolls        3x2  hats  7x2  birds        2x2  hats 


7.   Memorize  the  table. 


Table  of  2»s 


1x2=    2 

6x2  =  12 

2x2=   4 

7x2  =  14 

3x2=   6 

8x2  =  16 

4x2=   8 

9x2-18 

5x2  =  10 

10x2  =  20 

8.   Multiply  each  number  outside  the  circle  by  2. 


I 


Oral  and  Written]      MULTIPLICATION  25 

\     1.   How  many  are  two  7's  ?  two  lO's  ? 

2.  Write  these  two  problems  in  two  other  ways. 

3.  How  many  are  two  34's  ?     This  may  be  written : 

34  +  34  =  68,  or  34 

4-  34     The  sum  of  two  34's  is  68. 

68,  sum. 
t     4.   A  shorter  process  for  finding  two  34's  is  by  multi- 
plication ;  written  thus,    34  Write  the  multi- 

^  ^  plier  2  under  the 

68  right-hand  figure 

of  the  number  to  be  multiplied,  which  is  34.  Beginning 
at  the  right,  say  2x4  =  8.  Write  8  in  ones'  place  in 
the  answer.  2x3  =  6.  Write  6  in  tens'  place  in  the 
answer.    The  result  is  68.    Test  by  addition,  34  +  34  =  68. 

Multiply,  and  test  by  addition  : 

a  b  c  d  e  f 

23     54     53     64     71     62 

2      2      2      2      2      2 


6.  40  81  94  70  63  53 
_2  _^  _2  _2^  _2  _2 

7.  93  72  62  53  82  91 

2  2  2  2  2  2 


44 

32 

83 

24 

84 

74 

2 

2 

2 

2 

2 

2 

11 

73 

22 

33 

92 

44 

2 

2 

2 

2 

2 

_2 

26  FIRST  AND  SECOND   YEAR   [Oral  and  Written 

DIVIDING   BY  2 

^'  II  II  II  II  II  Count  the  splints  by  2's. 
How  many  times  must  two  splints  be  taken  to  have 
10  splints  ?     10  splints  contain  2  splints times. 

2.  6  contains  2  times.      8  contains  2  

times.     12  contains  2 times. 

3.  Into  bow  many  groups  of  two  each  may  10  be 
divided  ?     10  divided  by  2  equals  5,  written 

10  -^  2  =  5,  or  2)10.     The  sign  -^  is  read  divided  by. 
5 

Read,  and  give  answers : 

4.  4-2;  6-h2;  8-^2;  10^2. 

5.  2)8;  2)10;  2}6 ;  2]1_2. 

6.  Divide  24  by  2. 

2  is  contained  in  2  tens,  1  ten  time; 
2)24       write  1  in  tens'   place.     2  is  contained  in 
12       4  ones,  2  times;  wTite  2*  in  ones'  place. 
The  answer  is  12. 

Find  the  answers : 

a  b  c  d  e 

7.  2)22  2)24  2)_26  2)_44  2)20 

8.  2)28  2)40  2)48  2)42  2)_46 

9.  2)_62  2)_66  2)60  2)64  2)_68 
10.  2)80^            2)_84           2)88            2)_86            2]82 


Oral]  MEASURING   LENGTH  27 

MEASURING  LENGTH 

For  this  exercise  the  teacher  should  secure  a  foot  rule  and  a  yard 
stick. 

1.  Examine  a  foot  rule.  Observe  that  it  is  divided 
into  12  equal  spaces.  Each  space  is  called  one  inch. 
A  foot  rule  is  therefore  12  inches  long. 

2.  The  following  represents  a  foot  rule,  although  it 
is  only  one  fourth  the  real  length.  Count  the  number 
of  inch  spaces. 

-^+hH-H'.l'M:^MIUI'|ij,|ilWMi.|i|i^i|i.|iUcJliyi|A| 


3.  Cut  from  cardboard  a  foot  rule  and  mark  the 
inches  on  it. 

4.  With  the  rule  draw  a  line  1  inch  long ;  4  inches 
long. 

5.  How  many  inches  equal  J  of  a  foot  ?  J  of  a  foot  ? 
1  of  a  foot  ? 

6.  Draw  an  oblong  12  inches  long  and  8  inches 
wide.     How  many  inches  is  it  around  the  oblong  ? 

7.  Draw  a  2-inch  square.  How  many  inches  is  it 
around  the  square  ? 

8.  Measure  a  yard  stick  with  your  foot  rule.  This 
shows  that  there  are  3  feet  in  a  yard. 

9.  Mark  off  with  the  yard  stick  on  the  blackboard  a 
line  1  foot  in  length  ;  2  feet  in  length  ;  1  yard  in 
length. 

10.    How  many  feet  equal  2  yards  ?  J  of  a  yard  ? 


28  FIRST   AND   SECOND  YEAR  [Written 

REVIEW 

1.  A  man  paid  $  80  for  2  cows.     How  many  dollars 
did  each  cost  ? 

2.  A  family  bought  48  pints  of  milk  in  a  month. 
How  many  quarts  did  they  buy  ? 

3.  How  much  will  2  lb.  of  tea  cost  at  40^  a  pound  ? 

4.  How  many  2-cent  stamps  can  be  bought  for  64 
cents  ? 

5.  Eva  paid  86  cents  for  2  yards  of  linen.     What 
was  the  cost  of  1  yard  ? 

6.  If  Ruth  takes  2  piano  lessons  every  w^eek,  how 
many  does  she  take  in  44  weeks  ? 

7.  A  girl  is  14  years  old.     Her  brother  is  twice  as 
old.     How  old  is  her  brother  ? 

8.  How  many  pints  are  there  in  44  quarts  ? 

9.  If  a  clerk  earns  $  44  a  month,  how  much  will  he 
earn  in  2  months  ? 

10.  Dick  has  68  cents.     He  gives  35  cents  to  Kate. 
How  many  cents  has  he  left  ? 

11.  If  molasses  costs  14  cents  a  pint,  how  much  will 
a  quart  cost  ? 

Find  the  cost  of : 

12.  2  pieces  of  soap  at  10  cents  a  piece. 

13.  2  pounds  of  butter  at  24  cents  a  pound. 

14.  2  dozen  lemons  at  12  cents  a  dozen. 

15.  2  yards  of  muslin  at  11  cents  a  yard. 


PART  II  — THIRD  YEAR 
READING  AND  WRITING   NUMBERS 

1.  Count  to  one  hundred.  One  hundred  is  written  100. 

2.  Count  to  one  hundred  one,  written  101. 

3.  Write  in  figures  :  one  hundred  four ;  one  hundred 
five ;  one  hundred  seven. 

4.  Read,  then  write  in  words :  103,  105,  107,  109. 

5.  Add  100  to  100.  The  sum  is  two  hundred,  writ- 
ten 200.  Add  200  to  100.  The  sum  is  three  hundred, 
written  300. 

6.  Read,  then  write  in  words :  400,  500,  601,  700, 
802,  900,  501,  404. 


Read: 
a 
7.  109 

6 
309 

e 

506 

d 

836 

e 

707 

8.  110 

310 

340 

741 

888 

9.  112 

311 

765 

952 

999 

The  largest  number  that  can  be  written  with  three 
figures  is  999.  The  next  number  is  one  thousand, 
written  1000. 


Write  in  figures : 

10.  Two  thousand. 

11.  Five  thousand. 

12.  Six  thousand. 


13.  Seven  thousand. 

14.  Eight  thousand. 

15.  Nine  thousand. 


29 


30  THIRD  YEAR  [Oral  and  Written 

16.  Add  1  to  1000.  The  sum  is  one  thousand  one, 
written  1001. 

Write  in  figures : 

17.  One  thousand  two.  20.  One  thousand  seven. 

18.  One  thousand  nine.  21.  One  thousand  eight. 

19.  One  thousand  six.  22.  One  thousand  three. 

The  first  figure  on  the  right  is  called  the  ones'  figure ; 
the  next  is  called  the  tens'  figure ;  the  next  is  called 
the  hundreds'  figure ;  the  next  is  called  the  thousands' 
figure.  The  tens  are  always  read  as  so  many  ones. 
Thus,  1625  is  read,  "  1  thousand,  6  hundred,  25."  In 
25,  the  2  tens  are  read  as  20. 


] 

Read,  then  write : 

23. 

a 
1025 

6 
2040 

c 
7028 

d 
1010 

e 
8099 

24. 

1125 

2141 

9208 

1011 

8999 

25. 

1139 

3005 

6721 

2111 

9999 

26. 

2014 

4020 

6099 

7509 

8001 

Write  as  one  number  : 

27.  6  hundreds,  4  tens,  8  ones. 

28.  8  thousands,  5  hundreds,  3  tens,  3  ones. 

29.  4  thousands,  0  hundreds,  8  tens,  5  ones. 

30.  5  thousands,  0  hundreds,  0  tens,  9  ones. 

31.  9  thousands,  4  hundreds,  0  tens,  5  ones. 


Oral  and  Written] 


ADDITION 


81 


»K  ADDITION 

^^  (Review  pages  17  to  20) 

1.    Count  from  2  to  100  by  2's. 
2.    Count  from  1  to  101  by  2's. 
1^  3.    Count  from  3  to  102  by  3's. 

4.  Count  from  4  to  100  by  4's. 

5.  Count  from  1  to  101  by  4's. 

6.  Add  the  number  in  the  cen- 
ter to  each  number  outside  the  circle. 

7.  Add  3  to  each  of  the  following  numbers ;  then  4 ; 
then  5 : 


m 


24 

34 

44 

55 

65 

75 

36 

46 

66 

66 

76 

86 

47 

67 

27 

38 

58 

78 

Find  sums. 

Test 

by  adding 

downwards : 

a 

6 

C 

d 

e 

8.  23 

32 

42 

45 

51 

13 

23 

32 

51 

42 

43 

43 

44 

54 

14 

9.  44 

21 

53 

32 

31 

55 

32 

32 

24 

24 

33 

12 

43 

32 

32 

The  process  of  uniting  two  or  more  numbers  to  form 
one  number  is  called  addition. 

The  numbers  united  are  called  addends. 

The  answer  in  addition  is  called  the  sum  or  amount. 


32 


THIRD   YEAR 


[Written 


ADDITION 

1.   Add  234,  359,  and  266. 

234  =  2  hundreds  -f  3  tens  +  4  ones 
359  =  3  hundreds  +  5  tens  +  9  ones 
266  =  2  hundreds  +  6  tens  4-  6  ones 
859  =  7  hundreds  +  14  tens  +  19  ones. 

19  ones  =  1  ten  and  9  ones.  Write  the  9  in  ones* 
place  and  carry  the  1  ten  to  tens'  place.  14  tens  +  1 
ten  =15  tens.  Write  the  5  in  tens'  place  and  carry 
the  1  to  hundreds'  place.  7  hundreds  +  1  hundred  = 
8  hundreds. 

Write  from  dictation,  then  add  and  test : 


a 

6 

c 

d 

e 

/ 

2. 

234 

230 

101 

231 

301 

243 

326 

325 

304 

405 

226 

206 

434 

265 

376 

568 

304 

306 

3. 

405 

304 

604 

400 

291 

905 

304 

349 

787 

697 

743 

634 

296 

200 

842 

345 

456 

393 

4. 

623 

344 

23 

509 

20 

502 

5 

593 

906 

5 

102 

205 

340 

25 

25 

820 

67 

50 

5. 

708 

931 

68 

7 

423 

791 

55 

67- 

834 

751 

92 

8 

634 

8 

436 

534 

899 

958 

Written] 


I 


ADDITION 
ADDITION 


33 


Add  rapidly : 

abcdefgh 

1.  54321987 
98632052 
01256267 
18043616 
83685638 
76505981 
25998273 
69310437 


j      k       I      m     n 


6  6  8 

7  3  7 
9     0  3 

8  3  9 
3  4 
9  6 
9  3 
0  5 


3  2 

5  3 

7  3 

8  0 

6  5 
0  8     6 

8  9     5 

9  4     3 


300 

5 
794 
896 

25 


29 
330 

57 

8 

901 


6 
306 

27 

407 

92 


602 
74 

909 
40 
29 


90 
67 
80 
395 
74 


Write  from  dictation,  then  add : 

a 

6 

c 

d 

e 

/ 

9 

2.  305 

542 

740 

8 

70 

79 

500 

79 

67 

90 

48 

84 

342 

7 

6 

500 

708 

600 

395 

9 

48 

394 

9 

502 

540 

4 

805 

6 

3.  562 

807 

60 

536 

28 

42 

62 

9 

58 

547 

67 

906 

790 

203 

645 

6 

44 

25 

627 

7 

636 

834 

526 

782  ■ 

981 

8 

856 

93 

67 
500 
395 

70 
5 


34  THIRD   YEAR  [Written 

ADDITION 

1.   Find  the  sum  of  2430,  4307,  and  68. 
2430  =  2  thousands  +  4  hundreds  +  3  tens  +    0  ones 
4307  =  4  thousands  +  3  hundreds  +  0  tens  -f-    7  ones 
68  =  0  thousands  +  0  hundreds  +  6  tens  4-    8  ones 
6805  =  6  thousands  +  7  hundreds  +  9  tens  H-  15  ones. 

15  ones  =  1  ten  +  5  ones.  1  ten  +  9  tens  =  10  tens 
or  1  hundred.  1  hundred  +  7  hundreds  =  8  hundreds. 
4  thousands  +  2  thousands  =  6  thousands. 

Write  from  dictation,  then  add : 


2. 


a 

b 

C 

d 

e 

23 

378 

298 

1008 

603 

604 

49 

342 

49 

2798 

3068 

3067 

6781 

706 

6987 

1304 

2004 

4987 

•  3740 

6425 

279 

3050 

.   9 

609 

4020 

6000 

50 

807 

4203 

205 

200 

674 

5002 

6001 

1347 

6870 

5475 

64 

21 

3006 

2 

2681 

370 

2102 

2904 

3078 

5004 

4274 

3478 

799 

2690 

79 

5007 

9 

6094 

5.  2  +  3  +  7  +  9  +  6=?        7.    7  +  6  +  5  +  2  +  6  +  7=? 

6.  6  +  0  +  7  +  8  +  5=?        8.    5  +  4  +  3  +  8  +  6  +  9=? 


Written]  ADDITION  35 

I^^K  ADDITION 

l^^vi^rite  from  dictation,  then  add  : 

■^       1.    Twenty-five ;    two   hundred    twenty-five ;    three 
hundred  fifty. 

If      2.    Four   hundred   two;    seventy-three;    nine;    five 

hundred  sixty. 
IB       3.    Four  thousand  twenty;    six  hundred  six;    five. 

4.  Six  hundred   ninety;   ten;    three  hundred;    two 
thousand  four. 

5.  Two    hundred    eighty ;      nineteen ;      six ;      one 
thousand. 

6.  230  +  65  -f-  100  +  405. 

7.  300  +  9  +  25 -f  500. 

8.  65^  +  10^+100^  +  1000^. 

9.  $  42  +  $  504  +  $  105  +  $  3. 

10.  24  pt.  +  120  pt.  +  7  pt.  +  36  pt. 

11.  1000  qt.  +  14  qt.  +  135  qt.  +  10  qt. 

12.  174  pk.  +  130  pk.  +  5  pk.  +  800  pk. 

13.  1200  in.  +  10  in.  +  100  in.  +  20  in. 

14.  60  dimes  +  4000  dimes  +  4  dimes  +  300  dimes. 

15.  16.  17.  18 

2000  hours  1370  minutes  40  gallons  409  days 

146  hours  234  minutes  209  gallons  3090  days 

9  hours  30  minutes'  2900  gallons  9  days 

3472  hours  605  minutes  4  gallons  374  days 


36  THIRD   YEAR  [Written 

ADDITION 

Read  and  solve : 

1.  2465  +  3642  +  4612  +  5534  +  6342  =  ? 

2.  4756  +  3254  +  4321  +  4132  +  3536  =  ? 

3.  4234  +  3512  +  2435  +  1543  +  2453  =  ? 

4.  5243  +  2453  +  3215  +  4123  +  4231  =  ? 

5.  6314  +  1355  +  2652  +  1623  +  3245  =  ? 

6.  7664  +  2845  +  6246  +  3664  +  4554  =  ? 

7.  6050  +  4004  +  1804  +  4536  +  6143  =  ? 

8.  3652  +  4630  +  5672  +  3867  +  5468  =  ? 

9.  4876  +  6724  +  4116  +  3442  +  4162  =  ? 

10.  3640  +  4466  +  7201  +    404  +    162  =  ? 

11.  A  carpenter  had  23  men  and  hired  13  more. 
How  many  had  he  then  ? 

12.  Mr.  Jones  deposited  $  123  in  a  bank  on  Monday; 
$232  on  Tuesday;  and  $321  on  Wednesday.  How 
much  did  he  deposit  in  the  three  days  ? 

13.  A  ship  sailed  223  miles  the  first  day,  320  miles 
the  second,  and  231  miles  the  third.  How  many  miles 
did  it  sail  ? 

14.  A  farmer  raised  230  bushels  of  wheat,  122  bush- 
els of  corn,  112  bushels  of  oats,  and  323  bushels  of  rye. 
How  many  bushels  of  grain  did  he  raise  ? 

15.  Mrs.  Foster  bought  a  bedroom  set  of  furniture  for 
$  125,  a  piano  for  $  350,  curtains  for  $  52,  pictures  for 
$  128,  and  a  rug  for  $  23.    How  much  did  they  all  cost  ? 


SUBTRACTION 

SUBTRACTION 

(Review  pages  21  to  S 

Give  differences: 


1^ 


Give  answers  quickly : 


37 


X      7 

6 

5 

4 

13 

8 

9 

11 

10 

1  -4 

-5 

-2 

-3 

-8 

-4 

-5 

-3 

-3 

2.  13 

6 

8 

9 

7 

10 

12 

11 

8 

-6 

-3 

-3 

-7 

-2 

-7 

-4 

-5 

_  0 

3.    8 

9 

7 

15 

5 

12 

11 

17 

8 

-6 

-8 

-5 

-7 

-4 

-9 

-7 

-9 

-7 

4.   9 

13 

8 

9 

10 

12 

11 

12 

7 

-6 

-5 

-5 

-2 

-8 

-7 

-4 

-6 

-6 

5.  13 

14 

10 

12 

9 

10 

11 

12 

15 

-9 

-8 

-9 

-2 

-3 

-4 

-8 

-8 

-8 

6.   16 

15 

13 

14 

15 

16 

14 

12 

11 

-8 

-9 

-7 

-7 

-6 

-9 

-9 

-3 

-6 

7. 

8-3, 

18-3; 

28-3, 

48-3, 

58-3; 

8. 

11-4, 

21-4; 

31-4, 

41-4 

51-4; 

9. 

9-5, 

49-5; 

59-5 

89-5 

69-5; 

10. 

7-6, 

,17-6; 

27-6; 

37-6, 

47-6; 

11. 

13-7 

,  23-7; 

33-7, 

43-7, 

53-7; 

12. 

15-8, 

25-8; 

35-8 

,  45-8 

,  55-8; 

13. 

26-9 

;  36-9; 

46-9 

;  56-9 

;  66-9; 

88-3, 
61-4. 
79-5. 
97-6. 
83-7. 
75-8. 
96-9. 


38  THIRD   YEAR  -  [Written 

SUBTRACTION 

1.  From  83  subtract  35. 

83  =  8  tens  +  3  ones,  or  7  tens  +  13  ones 
35  =  3  tens  +    5  ones 

48  =  4  tens  +    8  ones. 

Since  5  ones  cannot  be  taken  from  3  ones,  take  1  ten 
( =  10  ones)  from  the  8  tens  (leaving  7  tens)  and  add 
it  to  the  3  ones,  making  13  ones.  13  ones  less  5  ones 
equal  8  ones.  7  tens  (remaining)  less  3  tens  equal  4  tens. 
Before  subtracting,  the  work  may  be  expressed  thus  : 
We  think:  "5  from  13  leaves  8j  3  from  7  ^  ^^ 
leaves  4 ;  48."  8  3 

Test  — 48  +  35  =  83.  3_5 

The  process  of  finding  the  difference  between  two 
numbers  is  called  subtraction. 

The  number  from  which  we  subtract  is  called  the 
minuend;  the  number  subtracted  is  called  the  subtra- 
hend ;  the  result  is  called  the  difference  or  remainder. 

Subtract,  and  test  each  result : 

a  b  c  d  e  f  g 

2.  63    92    84    57    84    34    91 
27    69    39    38    49    17    54 


3.  48 

74 

81 

63 

92 

•  86 

84 

29 

47 

29 

44 

74 

58 

45 

4.  55 

80 

31 

61 

21 

34 

47 

19 

27 

18 

57 

13 

16 

38 

Written] 

SUBTEAOTION 

38 

IB     Subtract  and  test 

: 

1      ^ 

H     1.   769 
IB          374 

6 

819 
568 

c 

346 

94 

d 
665 
374 

e 
749 

298 

/ 

864 
539 

n     2.   332 
11          ^^^ 

748 
339 

552 
429 

175 

68 

729 
549 

534 
360 

3.  Make,  solve,  and  test  200  problems  like  the  above. 

4.  From  803  subtract  576. 

7  9  13 

803  =  7  hundreds  +  9  tens  +  13  ones 

576  =  5  hundreds  +  7  tens -f-    6  ones 

2  2  7  ==  2  hundreds  -h  2  tens  +    7  ones. 

Take  1  hundred  from  8  hundreds ;  this  leaves  7  hun- 
dreds. 1  hundred  equals  10  tens.  Take  1  ten  from  10 
tens ;  this  leaves  9  tens.  1  ten  and  3  ones  are  13  ones. 
803  then  is  equal  to  7  hundreds,  9  tens,  and  13  ones. 
13  ones  —  6  ones  =  7  ones ;  9  tens  —  7  tens  =  2  tens;  7 
hundreds— 2  hundreds  =5  hundreds.     Answer,  227. 

Read,  then  subtract  and  test : 

a                     b                     c  d  e 

5.  8404           7604           5041  5202  7011 
3625           4896           1979  1824  4583 

6.  7024  8401  5401  8704  4087 
3767           4574           2519            6247  1069 

7.  Subtract  187  from  9234;  then  take  187  from  each 
successive  remainder,  until  the  final  remainder  is  7364. 


40  THIRD   YEAR  [Written 

SUBTRACTION 

1.  From  700  take  264. 

6  9  10 

700=6  hundreds  +  9  tens  +  10  ones 
264  =  2  hundreds  +  6  tens  +  4  ones 
436  =  4  hundreds  H-  3  tens  +    6  ones. 

a  bed  6       / 

2.  500    600    900    400    800    700 

154    247    678    197    372    309 


3. 

300 

700 

600 

800 

200 

400 

263 

288 

327 

561 

181 

397 

4. 

604 

809 

701 

902 

606 

705 

160 

341 

202 

720 

408 

496 

5. 

609 

501 

303 

806 

903 

703 

285 

209 

180 

199- 

287 

587 

6. 

706 

801 

704 

560 

601 

890 

567 

560 

395 

297 

269 

798 

7. 

2042 

4106 

5001 

8012  ■ 

7020 

1407 

1012 

2014 

3014 

5707 

2904 

1289 

8. 

7018 

5080 

9001 

8304 

4400 

1604 

4009 

3107 

3082 

5012 

3870 

1397 

I 


ritten] 

SUBTRACTION- 

41 

SUBTRACTION 

Subtract : 

a 

b 

c 

d 

e 

1.  6432 

7244 

6475 

7994 

8641 

4176 

5371 

3879 

3877 

1282 

2.  4531 

4351 

4234 

2432 

2134 

1522 

1543 

1235  ■ 

1344 

1545 

3.  5423 

4215 

3254 

3524 

8231 

2545 

1567 

1565 

1566 

4743 

4.  4253 

3231 

5453 

8121 

6414 

1464 

1865 

1974 

3642 

3892 

M 


5.  412  boys  and  325  girls  were  enrolled  in  a  school. 
How  many  more  boys  than  girls  were  enrolled  ? 

6.  Harry  has  42  chickens.  After  he  has  fed  15  of 
them,  how  many  chickens  remain  to  be  fed  ? 

7.  John's  home  is  132  miles  from  New  York,  and 
Mary's  home  is  341  miles  from  New  York.  How  many 
miles  farther  from  New  York  does  Mary  live  than  John  ? 

8.  The  perimeter  or  distance  around  a  dining  table 
is   28  feet   and  that  of   the   library  table  is  21  feet. 

ind  the  difference  in  the  perimeters. 

9.  An  automobile  ran  312  miles  one  week  and  145 
miles  the  next  week.  How  many  more  miles  did  the 
automobile  run  the  first  week  than  the  second  week  ? 


42  THIRD   YEAR  [Written 

ADDITION  AND   SUBTRACTION 

1.  In  the  Central  School,  there  are  398  pupils ;  in 
the  Garfield  School,  1045,  and  in  the  Holmes  School, 
2306.     How  many  pupils  are  there  in  the  three  schools? 

2.  Mr.  Adams's  home  cost  $  4370,  and  Mr.  Boyd's  cost 
$3745.     Find  the  difference  in  the  cost  of  their  homes. 

3.  John  lives  5906  feet  from  his  school,  and  Thomas 
lives  2194  feet  nearer  the  school  than  John.  How  far 
does  Thomas  live  from  the  school  ? 

4.  Bertha  counted  the  people  in  four  parades.  Tn  the 
first  there  were  208 ;  in  the  second,  890 ;  in  the  third, 
1506  ;  and  in  the  fourth,  1781.  How  many  were  there 
in  all  ? 

5.  In  two  city  schools,  boys  parade  as  soldiers.  In 
the  first  school  there  are  1790  boys ;  in  the  second 
school  279  boys  less  than  in  the  first.  How  many 
boys  are  there  in  the  second  school  ? 

6.  A  merchant  sold  for  the  fourth  of  July,  3706 
small  flags,  1712  larger  flags,  and  19  flags  for  flag 
poles.     How  many  flags  did  he  sell  ? 

7.  In  counting  the  steps  to  school,  Joseph  took  1370, 
and  Harvey  took  940  less  than  Joseph.  How  many 
steps  did  Harvey  take  ? 

8.  A  street-car  conductor  collected  103  fares  on  the 
first  trip,  72  on  the  second,  trip,  176  on  the  third  trip, 
and  39  on  the  fourth  trip.  How  many  fares  did  he 
collect  ? 


Oral] 


MULTIPLICATION 


43 


MULTIPLYING  BY  3 

1.  Count  by  2's  to  36  ;  by  3's  to  36. 

2.  How  many  are  3  +  3,  or  two  3's? 
or  three  3's  ?     3  +  3  +  3  +  3,  or  four  3's  ? 

3.  Three  3's  are ;  five  3's  are  — 

six  3's  are ;  nine  3's  are . 

p     4.   How  many  are  7x3?     5x3? 

5.   Build  the  table  of  3's  to  12  x  3  thus : 


3  +  8  +  3, 

3 

3  3 

333 

8333 

3  3  3  3  3 

3  3  3338 

Write  the  sum  of  each  column  beneath  it.       3  3  3  3  3  3  3 
Look  at  each  column  and  say,  1x3  =  3 ; 
2x3  =  6;  3x3  =  9;  etc. 

6.  3x8  =  8x?  3x5  =  5x?  9x8  =  3x? 

Table  of  3's  7.   Memorize  the  table. 


1x3=   3 

7x3  =  21 

2x3=   6 

8x3  =  24 

3x3=   9 

9x3  =  27 

4x3  =  12 

10x3  =  30 

5x3  =  15 

11x3  =  33 

6x3  =  18 

12x3  =  36 

Multiply  at  sight: 

9.     4        2        5 

3        3        3 

7 
3 

9 
3^ 

8. 

8 
3 

Give 

6 

3 

products. 

10       11 

3        3 

10.  12      20      40 
3        3        3 

30 
3 

50 
3 

70 
3 

60 
_3 

90      80 
3        3 

44 


THIRD   YEAR 


[Written 


MULTIPLYING   BY  3 

1.  Multiply  65  x  3. 
3x5  ones  =  15  ones,  or  1  ten 

and  5  ones.     Write    the  5  ones  in 
ones'  place.      3x6  tens  =  18  tens ; 
18  tens  +  the  1  ten  of  the  15  ones 
=  19  tens.     The  answer  is  195. 
We  think  :  "  3  times  5  =  15;   3  times 

18  ;  18  4- 1  =  19."     Product  195. 

The  number  multiplied  is  called  the 

multiplicand.    The  number  showing  how 

.many  times  the  multiplicand  is  taken  is 

called  the  multiplier.     The  result  m  multiplication  is 

called  the  product. 

Multiply,  and  test  each  product  by  addition : 

a  he  d  e 

2.  45  75  66  74  86 

3  3  3  3  3 


Multiplicand 

65 

Multiplier 

3 

Product 

195 

Test.      65 

65 

6  = 

65 
195 

mi 

3.   135 
3 


236 
3 


5.   209 
3 


6.    132 
3 


105 
3 

409 
3 

146 
3 

145 
3 


216 
3 

237 
3 

284 
3 

298 
3 


308 
3 


207 
3 


258 

189 

3 

3 

167- 

248 

3 

3 

276 

287 

3_ 

3 

Written] 


MULTIPLICATION 


45 


I 


MULTIPLICATION   OF   CONCRETE   NUMBERS 

Numbers  that  name  objects  are  concrete;  as  6  apples, 
3  boys,  5  yards. 

Numbers  that  do  not  name  objects  are  abstract ;  as 
7,  9,  3. 

In  multiplying  concrete   numbers,  the   multiplicand 
and  the  product  have  the  same  name. 

The  multiplier  is  always  an  abstract  number. 

1.   How  many  oranges  are  there  in  3  dozen  ? 

12  oranges  in  1  doz. 
3  3  X  12  oranges  =  36  oranges. 


36 

oranges  in 

3  doz. 

Multiply : 

a 
2.   46jzf 

3 

h 

24  cans 
3 

c 

56  balls 
3 

d 

28  qt. 
3 

3. 

25  ft. 
3 

28  pt. 
3 

47  gal. 
3 

82  yd. 
3 

4. 

96  da. 
3 

84  min. 
3 

75  poles 
3 

48  nfiles 
3 

5. 

93  trees 
3 

88  dimes 
3 

52  eggs 
3 

93  birds 
3 

6. 

86  wheels 
3 

48  cakes 
3 

72  pies 
3 

197  nuts 
3 

46 


THIRD   YEAR 


[Oral 


MULTIPLYING  BY  4 

1.  Count  by  4's  to  12  ;  to  24 ;  to  36 ;  to  48 

2.  How  many  are  4  +  4,  or  two  4's  ? 


three  4's  ?     4  +  4  +  4  +  4,  or  four  4's  ? 

3.  Five  4's  are ;   six  4's  are . 

4.  How  many  are  2x4?   4x4?    5x4? 

5.  Build  the  table  of  4's  to  12  x  4  thus : 


Write  the  sum  of  each  column  beneath  it. 
Look  at  each  column  and  say,  1x4  =  4; 
2x4  =  8;  3x4  =  12;   etc. 

6.  4x8=?x4     9x4  =  4x?    6x4  =  ?x6. 

7.  Memorize  the  table.  Table  of  4's 


4  +  4  +  4,  or 

4 

44 

444 

4444 

44444 

444444 


8.  Give  products. 

9.  Give  products  at  sight 
5  7  9  11 
4         4  4  4 


1x4=   4 

7x4  =  28 

2x4=   8 

8x4  =  32 

3x4  =  12 

9x4  =  36 

4x4  =  16 

10x4  =  40 

5x4  =  20 

11x4  =  44 

6x4  =  24 

12x4  =  48 

12 
4 


10.  4x5    3x8    4x10    4x7    2x9 

11.  3x6    4x12   3x2    3x10   4x4 

12.  4  X 11   4x2    3  X  10    4x9    4x8 


Oral  and  Written]    MULTIPLICATION  47 

PRACTICAL  PROBLEMS 

1.  Emma  has  4  pieces  of  ribbon  of  10  yards  each. 
How  many  yards  has  she  in  all  ? 

2.  How  many  lemons  are  there  in  4  dozen  ? 

3.  How  far  can  you  ride  in  4  hours  in  a  carriage 
that  travels  on  an  average  of  4  miles  an  hour  ? 

4.  How  many  pecks  are  there  in  11  bushels  ? 

5.  At  10^  a  quart,  how  much  will  1  gal.  oil  cost? 

6.  How  many  days  are  there  in  4  weeks  ? 

Multiply,  and  test  by  addition  : 

a  b  c  d  e 

7.  165  238  369  748  569 

4:  4:  4:  4:  4 


8. 

293 
4 

687 
4 

574 
4 

862 
4 

738 
4 

9. 

786 
4 

934 

4 

867 
4 

279 
4 

184 
4 

10. 

915 
4 

846 
4 

739 
4 

862 
4 

475 
4 

11. 

886 
4 

995 
4 

774 
4 

663 
4 

552 
4 

Give  products  at  sight: 

12.  4x20       4x50       4x80      4x25       4x17 

13.  4x30      4x60       4x90      4x15       4x18 


48  THIKD  YEAR  [Written 

PRACTICAL  PROBLEMS 

1.  If  a  sail  maker  uses  18  yards  of  cloth  in  a  main- 
sail, how  many  yards  would  he  require  for  3  such  sails  ? 

2.  If  it  takes  Helen  24  minutes  to  hemstitch  a  collar, 
how  many  minutes  will  it  take  for  4  collars  ? 

3.  A  man  bought  4  lots  at  $475  each.     How  much 
did  they  cost  ? 

4.  Mr.  Home  made  3  payments  of  $645  each  for 
his  house.     What  was  the  cost  of  his  house  ? 

5.  If  each  pupil  in  a  school  of  658  has  4  books,  how 
many  books  have  they  all  ? 

6.  A  drover  bought  3  horses  at  $235  each.     How 
much  did  he  pay  for  all  ?  ^ 

7.  A  farmer  sold  276  sheep  at  $4  a  head.     How 
much  did  he  receive  for  all  ? 

8.  If  a  train  runs  476  miles  in  a  day,  how  far  can 
I  travel  on  it  in  3  days  ? 

9.  A  ship  sailed  364  miles  each  day.     How  far  did 
it  sail  in  4  days  ? 

10.  A  car  carries  60  persons.     How  many  persons 
will  4  such  cars  carry  ? 

11.  How  many  acres  are  there  in  4  farms,  if  each 
farm  contains  175  acres  ? 

12.  At  $  15  each,  how  much  will  3  paintings  cost  ? 

13.  How  many  boys  are  playing  soldier,  if  there  are 
4  rows  and  16  boys  in  each  row  ? 


Oral  and  Written] 


DIVISION 


49 


r 


DIVIDING  BY  3 

1.  Count  by  3's  to  9;  to  18;  to  30  ;  to  36. 

2.  How  many  times  does  6  contain  3?     ||| 

3.  Show  by  separating  into  groups  : 


12  contains  3 
18  contains  3 


times 
times 


15  contains  3  — 
21  contains  3  — 


Give  quotients  at  sight : 


9 
24 


18^3 
30^3 


33^3 
21 -f- 3 


12^3 
36-^3 


-  times 

-  times 

27^3 
15^3 


5.  Divide  each  number  outside  the 
circle  by  3. 

6.  Find: 
I  of  27     1  of  30     1  of  36     i  of  15 
1  of  12     J  of  18     J  of  21     1  of  33 

7.  Compare  6  and  2  ;  thus :  6  is  3 
times  2.     2  is  i  of  6. 

The  number  divided  is  called  the  dividend. 

The  number  by  which  we  divide  is  called  the  divisor. 

The  answer  in  division  is  called  the  quotient. 

Divide  and  test : 

a  b  c  d  e 

8.  3)24_         3)36  3)27  3)30  3)21 


9.  3)393 
10.  3)150 


3)363 
3)900 


3)339 
3)660 


3)933 
3)693 


3)303 
3)369 


50  THIKD  YEAR  [Oral  and  Written 

1.  The  sign  -^  is  read  divided  by. 

2.  24^-7-3^  means  that  we  are  to  find  how  many 
times  3P  is  contained  in  24^;  thus:  3^)24^ 

8  times. 

Find  quotients : 

3.  82  days -^  2  days  9.  189  years  ^3  years 

4.  186  hours  ^  3  hours  lo.  244  roses  ^  2  roses 

5.  422  minutes  -^  2  minutes  ii.  664  cents  -^  2  cents 

6.  448  feet -^  2  feet  12.  336  quarts  ^3  quarts 

7.  249  inches -H  3  inches  13.  144  gallons -^  2  gallons 

8.  622  dollars -^2  dollars  14.  428  pints -5- 2  pints 

15.    24^^  3  means  that  we  are  to  find  one  third  of 
24 j^;  thus:  1  of  24 j^  equals  8^,  or  3)24^. 

8^ 

Find  quotients: 

16.  224  days  ^2  24.  844  gallons -f- 2 

17.  333cents-^3  25.  646  quarts -^  2 

18.  216  dollars -^  3  26.  969  pencils -^  3 

19.  622  birds -f- 2  27.  842  books -^  2 

20.  326  inches -^  2  28.  936  hours  ^3 

21.  219  hours -^  3  29.  288  pages -^  2 

22.  444  roses  -^  2  30.  428  pints  ^  2 

23.  468  minutes  ^  2  31.  639  pens  -^  3 


Written]  DIVISION  61 


r 


REMAINDER  IN   DIVISION 

1.  Divide  263  by  3. 

Divisor  3)263  Dividend         26  tens  -5-3  =  8  tens,  and  2  tens 

87  Quotient         (20    ones)    remaining.      Write 

Remainder  2    the  8  tens  in  the  tens'  place. 

20  ones  +  3  ones  =  23  ones.     23  ones  -^  3  =  7  ones,  and 

2  ones  remaining.     Quotient  87  ;  remainder  2. 

We  think :  "  3  in  26,  8  times,  and  2  remaining;  3  in  23, 
7  times,  and  2  remaining."     Quotient  87 ;  remainder  2. 

Test.  —  If  the  answer  is  correct,  then  3  x  87,  or  261, 
H-  2,  the  remainder,  will  equal  263,  the  dividend. 

Divide  and  test  by  2 ;  by  3 : 

a  b  c  d  e 

2.  265  864  786  624  7368 

3.  713  219  265  758  2457 

4.  Compare  12  ^  2  and  |  of  12 ;  12  -^  3  and  J  of  12. 

To  find  ^  of  any  numher,  divide  the  number  hy  2. 
To  find  -J-  of  any  numher,  divide  the  number  by  3. 

How  many  are : 

a  b  c 

5.  1  of  240  men  ?       J  of  171  balls  ?       J  of  $  7484  ? 

6.  1  of  717  feet  ?  i  of  216  mi.  ?  i  of  $  3927  ? 

7.  1  of  435  yd.  ?  ^  of  384  bu.  ?  i  of  $  8064  ? 

8.  1  of  759  gal.  ?  1  of  902  in.  ?  i  of  $  2160  ? 

9.  1  of  285  pk.  ?  1  of  405  f t.  ?  •     J  of  $  2754  ? 


[Oral  and  Written 


52  THIRD   YEAR 

DIVIDING  BY  4 

1.  How  many  are  four  2's  ?     4  in  8,  - 

2.  How  many  are  four  3's  ?     4  in  12, 

3.  How  many  times  does  16  contain  4? 

4.  20  contains  4,  times ;  24  contains  4, 


times. 
-  times. 


times ;  28  contains  4, 
times. 


times ;  32  contains  4, 


5.   36^4  =  ?    40-5-4  =  ?    44-f-4  =  ?    48-^4  =  ? 

36 


20 

/40 

36 44 

6.   Give  quotients.  7.   Give  parts. 

Divide,  and  test  by  multiplication: 


8.  4)268 

9.  4)3604 

10.  4)4693 

11.  4)5169 

12.  4)6981 

13.  4)3204 


h 

4)864 

4)9216 

4)5248 

4)2834 

4)1243 

4)4126 


c 

4)936 

4)3704 
4)9270 

4)6573 
4)6476 
4)3958 


4)468 

4)4008 

4)7354 

4)6291 
4)5034 

4)2976 


4)2240 
4)3246 

4)4687 
4)8473 
4)2075 
4)8169 


Written]  DIVISION  63 

DIVISION 

1.  Walter  had  48  baskets  of  fruit.  He  sold  an  equal 
number  to  4  different  buyers.  How  many  baskets  did 
each  buy  ? 

4)48  Xo.  of  baskets.  J  of  48  baskets  =  12  baskets. 

12  No.  of  baskets  to  each. 

2.  Mary  has  45  cents.  How  many  3  cent  oranges 
can  she  buy  with  her  money  ? 

3^  =  cost  of  1  orange     3^)45^ 

15  times,  or  15  oranges. 

3.  A  man  divided  property  valued  at  $  369  equally 
among  his  3  children.     How  much  did  each  receive  ? 

4.  Mr.  Bell  earned  $  396  in  3  months.  What  were  his 
monthly  wages  ? 

5.  Find  the  cost  of  1  bushel  of  wheat,  if  4  bushels 
cost  280  cents. 

6.  If  a  girl  sews  4  buttons  on  each  pair  of  gloves, 
how  many  pairs  has  she  finished  when  she  has  used 
468  buttons? 

7.  A  farmer  having  96  hogs  sold  one  third  of  them. 
How  many  did  he  sell  ? 

8.  In  a  car  containing  639  baskets  of  peaches,  one 
third  were  spoiled.     How  many  baskets  were  spoiled  ? 

9.  How  many  pound  boxes  can  be  filled  from  164 
quarter  pounds  of  candy  ? 

10.  When  molding  costs  15^  a  yard,  how  much  will 
1  foot  of  it  cost  ? 

1  ft.  =  J  of  a  yard  j  1  ft.  will  cost  i  of  15^,  or  5  cents. 


54  THIRD  YEAR         [Oral  and  Written 

UNITED   STATES   MONEY 

United  States  money  is  written  in  dollars  and  cents. 

A  period  (.),  named  a  ''decimal  point/'  is  placed  to 
the  right  of  dollars.  After  the  point,  cents  are  written 
in  two  places.  Thus,  5  dollars  and  25  cents  is 
written    $5.25. 

1.   Read:    $8.40;   $9.67;   $3.14;   $8.24;   $7.05. 

In  addition  and  subtraction  of  United  States  money, 
the  point  must  be  written  under  the  point,  dollars  under 
dollars,  and  cents  under  cents. 

Read  and  add : 

2.  $3.45  $2.24  $3.14  $3.62         $2.43 

2.61  3.36  1.35  2.45  3.25 

Add  across  and  in  columns : 

3.  $  2.24  +  $  3.25  +  $  6.42  +  $  2.56  4-  $  3.25  +  $  4.63  = 

4.  $  3.14  +  $  2.35  +  $  3.11  +  $  6.14  +  $  2.65  +  $  6.15  = 

5.  $  4.24  +  $  5.32  +  $  2.34  +  $  5.23  +  $  2.34  +  $  5.26  = 

Read  and  find  differences : 

a  h  c  d  e 

6.  $3.46  $3.25  $3.41  $6.11  $5.13 

1.25  2.74  2.56  2.65  2.65 

7.  $2  43  $3.25  $3.41  $6.11         $5.13 

1.47  1.46  2.16  5.26  2.56 

8.  Add  $4.25  and  $2.64.      lo.   Add  $  2.54  and  $  1.36. 

9.  Add  $  3.62  and  $  2.16.      ii.   Add  $  3.26  and  $  1.56. 


UNITED   STATES   MONEY  55 


UNITED   STATES  MONEY 

Read  and  add : 

abed 

1.    $246.25           $632.75           $327.56  $805.96 

318.75             738.49             928.89  613.73 

92.48             918.86             738.86  928.45 

18.64               29.94             198.37  56.91 

237.75             169.83               75.59  219.87' 


2. 

$178.84           $219.35 

$165.27 

$214.56 

6.92                 7.29 

86.15 

3.94 

175.49             216.87 

283.85 

69.47 

862.81             938.75 

395.94 

138.85 

219.97             139.49 

415.86 

475.27 

3. 

$  465.75  +  $  37.28  +  $  692.37  +  $  475.84  = 

=  ? 

4. 

$193.85+  $87.96+  $S 

175.84 +  $215.79  = 

=  ? 

S. 

$276.49 +  $29.49  +  $ 

49.86 +$936.93: 

=  ? 

6. 

$  475.98  +  $  18.07  +  $  126.92  +  $  214.85  ■■ 

=  ? 

+               + 

+ 

=  ? 

Subtract  and  test : 

a                           h 

c 

d 

7. 

$475.36           $435.24 

$438.64 

$821.42 

196.28             178.95 

195.73 

195.38 

8. 

$317.61           $124.15 

$326.47 

$412.49 

219.84               95.76 

158.96 

273.89 

9.   $246.37 -$174.75  lo.   $235.55 -$169.73 


5Q 


THIRD   YEAR 


[Oral 


MULTIPLYING  BY  5 

1.  Count  by  5's  to  10 ;  to  30 ;  to  45  ;  to  60. 

2.  How  much  are  two  5-cent  pieces  ?     2x5  =  ? 

3.  How  much  are  three  5-cent  pieces  ?     3x5=? 

4.  Tell  the  value  of  four  5-cent  pieces;  of  5  such 
pieces ;  of  6,  7,  8,  9,  10,  11,  12. 

5.  How  many  5's  are  there  in  10  ?  in  20  ?  in  30  ? 
60?  25?  35?  45?  55?  40?  50?  15?  ^ 

6.  Multiply   each    of    the    outside      ^^ 
iiumbers  by  5.      Change    the  number 
within   the  circle  to  4  and  multiply; 
then  to  3 ;  to  2.    Build  the  table  of  5's      ^ 
as  you  built  the  table  of  4's 

7.  Memorize  the  table. 

8.  Supply  the  missing 
numbers : 
2x5  =  ? 
4x  ?=20 
5x5  =  ? 
?  x5  =  35 
9x  ?  =  45 


5  is  ?  of  10 
?  is  1  of  20 
25  is  ?  X  5 
?  is  ^■  of  35 


Table  of  5's 

1x5=    5 

7x5  =  35 

2x5=10 

8x5  =  40 

3x5=15 

9x5  =  45 

4x5=20 

10x5=50 

5x5  =  25 

11x5  =  55 

6x5  =  30 

12x5  =  60 

I-  of  45  is  ? 

9.    Give  products  :  8  x  5  ; 
9x5;    3x5;    5x5;    7x5;    6x5;    12x5. 

10.    What  is  the  difference  in  value  between : 
3x$5and5x$3?  7x5  hats  and  5  x  7  hats? 

6x$5and5x$6?  2x4  books  and  4  x  2  books? 


Written] 


MULTIPLICATION 


57 


I 


MULTIPLICATION   OF   DOLLARS   AND   CENTS 

1.   Multiply  $3.65  by  3. 


$3.65 

3 

$10.95 


2.   Multiply  $  0.65  by  4. 
$0.65 


I 


$2.60 

Multiply : 
a 

4.  $3.50 
2 

5.  $7.04 
4 

6.  22^ 

3 


In  multiplying  dollars  and  cents,  place 
the  decimal  point  in  the  product  directly 
under  the  decimal  point  in  the  multipli- 
cand. Write  the  dollar  sign  before  the 
number  of  dollars. 

Multiply  70^  by  3. 
70^ 
3 
210^=  $2.10  (Why?) 


3. 


h 

$3.05 
4 

$0.60 
5 

5 


c 

$6.05 
3 

$0.08 
3 

261^ 
4 


d 
$9.40 
5 

74^2^ 
_£ 

5 


7.  How  much  will  3  pecks  of  peaches  cost  at  65^  a 
peck? 

8.  A  messenger  boy  delivers  4  messages  at  45^  each. 
How  much  does  he  earn  for  his  company  ? 

9.  May  gets  $  3.75  per  week  in  a  department  store. 
Find  her  wages  for  4  weeks. 


58 


THIRD   YEAR 


[Written 


PRACTICAL   PROBLEMS 

1.  How  many  seats  are  there  on 
each  side  of  the  car  ? 

2.  How  many  are  two  times  11 
seats  ? 

3.  The  conductor  collected  75  fares 
on  the  first  trip  and  87  fares  on  the  re- 
turn trip.  How  many  fares  did  he 
collect  ? 

4.  The  fare  is  5  cents.  How  much 
money  did  he  collect  on  both  trips  ? 

5.  A  lady  paid  for  herself  and  5 
children.  She  gave  the  conductor  a 
half  dollar.  How  much  change  should 
she  receive  ? 

6.  Each  seat  will  accommodate  two  persons, 
many  persons  can  be  seated  in  the  car  ? 

7.  The   conductor   earns    $2.50    in   a   day. 
much  does  he  earn  in  5  days  ? 

8.  The  motorman  is  paid  $2.75  a  day.  How  much 
does  he  earn  in  5  days  ?  How  much  more  does  he  earn 
in  a  day  than  the  conductor  ? 

9.  The  line  is  8  miles  long.  How  far  does  a  car  run 
in  making  5  round  trips  ? 

10.  On  one  trip  each  seat  was  occupied,  and  5  per- 
sons had  to  stand.  Ftud  the  amount  of  the  fares  for 
the  trip. 


How 


How 


Oral  and  Written] 


DIVISION 


69* 


rp  MULTIPLYING   BY  6 

1.    Count  by  6's  to  12;  to  24;  to  48;  to  60;  to  72. 
Build  the  table  of  6's. 

2.    How  many  6's  are  there  in  12  ?  in  18  ?   24  ?  36  ? 

48?  54?  60?  66?  72? 


Table  of  6 

's 

1 

x6  = 

6 

7 

x6  = 

42 

2 

x6  = 

12 

8 

x6  = 

48 

3 

x6  = 

18 

9 

x6  = 

54 

4 

x6  = 

24 

10 

x6  = 

60 

5 

x6  = 

30 

11 

x6  = 

66 

6 

x6  = 

36 

•12 

X  6  = 

72 

5.  Multiply  each  number  outside 
the  circle  first  by  3,  then  by  4,  then 
by  5,  then  by  6. 


3.  Memorize  the  table. 

4.  Compare  in  two  ways: 

Thus  6  is 

3  more  than 

3;  6  is 

2x3. 

6  and  3 

12  and  3 

6  and  4 

12  and  4 

6  and  5 

12  and  5 

4  and  2 

16  and  4 

outside     1 1  / 

-^^-^ 

3X 
4X 
5X 
6X 


Multiply  by  6;  by  5;  by  4;  by  3: 

h  c 

567  149 

295  293 

8.  978  869  687 

9.  207  890  903 


a 

6.  243 

7.  679 


10.    Give  products  at  sight : 
6  X  40  5  X  20  6  X  80 

6x70  5x35  5x32 


6  X  90 


x41 


4x71 


d 
759 

384 

825 
708 

5x50 
6x  25 
4x92 


e 
894 

679 

856 

605 

6x61 
6x42 
6x81 


60 


THIED  YEAR  [Oral  and  Written 


DIVIDING  BY  5 

1.  Count  by  5's  to  15  ;  to  25  ;  to  45  ;  to  50  ;  to  60. 

2.  ?  X  5  =  15      ?  X  5  =  20      ?  X  5  =  40 

3.  Give  answers : 
5-^5      15^5      50-^5      45-^5 

30-5      40-^5       35^5       10^5 
55-^5      60-^-5      25  H- 5      20^5 

25         ^0 

Division  may  be  indicated  in  three  ivays:  First,  8-^2; 
second,  2]|8  ;  third,  f .     Each  is  read  8  divided  by  2. 

4.  Read  and  solve : 
16  -f-  4  4}16 

¥  ¥- 

5.  ■  Divide  by  5  and  give  remainders : 
43       62       27       48       39       56       53 


¥ 

¥ 

¥ 

¥ 

¥ 

125 

324 

340 

2  84 

S4£ 

6.   Find  ^  of: 
420  men  375  hr. 

365  horses       180  da. 


Divide  and  test : 


7.  5)4225 

8.  5)5693 

9.  5)7024 


b 

5)7086 

5)4287 
5)9046 


825  pt. 
315  gal. 


c 

5)9275 

5)1364 
4:2753 


$415 
$630 


d 

5)4376 

5)7006 
5)4203 


14        27 

870  JJ' 
560/^ 

e 

5)8450 

5)7005 
5)2004 


Oral  and  Written]  DIVISION  61 

DIVIDING   BY  6 

1.    How  many  times  is  6  contained  in  12  ?   in  18  ? 
in  24?  in  48?  60  ?  54  ?  36  ?  66  ?  42  ?  72? 


2.    (iive  answers : 

42-5-6          60  ^  6          36  ^  6 

24^6 

48^6 

35  ^  5          48  -:-  4          J  of  35 

lof  42 

60^6 

6|48              6^60              6)54 

6)36 

6)30 

3.    Divide  each  number  by  6 : 

480                600                624 

540 

366 

720                618               246 

726 

612 

4.    Complete : 

15-i-6=  —  and  —  over.     6x8,-f?  = 

=  50     6x9,-t-?  =  59 

45  -i-  6  =  —  and  —  over.     ?  x  6,  -1-  2  = 

=  56     6x? 

',-1-3  =  45 

5.  Divide  by  5  and  give  remainders ;  then  by  6 : 
843  864               631               7235               8697 
675  293               845               4618               3256 
931  787               569               8627              4367 

6.  Compare  in  two  ways :  $  18  and  $  3  ;  $  36  and  $  6  ; 

35  books  and  5  books;  24  hats  and  4  hats;   42  lemons 
and  7  lemons;  45)^ and  5^. 

7.  Find  the  cost  of : 

6  oranges  at  18^  a  doz.  40  pears  at  4^  each. 

36  apples  at  2^  each.  18  eggs  at  10 j^  a  doz. 

8.  At  3^  apiece,  how  many  oranges  can  you  buy  for 
18^?  for  42^?  for  36^?  for  72)^? 


62  THIRD  YEAR  [Written 

PRACTICAL   PROBLEMS 

1.  Find  the  cost  of  5  yards  of  cloth  at  $  .75  a  yard. 

2.  Four  boys  deposited  in  the  school  bank  as  fol- 
lows: $4.25,  $6.93,  $4.34,  and  $6.05.  What  was  the 
entire  deposit  ? 

3.  Julia  went  to  the  store  with  a  twenty-dollar  bill. 
She  paid  75  cents  a  yard  for  6  yards  of  oilcloth,  and 
$  9.50  for  a  rug.     How  much  had  she  left  ? 

4.  A  box  contains  360  oranges.  If  ^  of  them  are 
bad,  how  many  good  ones  are  there  in  the  box  ? 

5.  At  36  cents  a  dozen,  how  much  will  5  dozen 
oranges  cost  ? 

6.  At  24  cents  a  dozen,  how  much  will  6  dozen 
oranges  cost  ?  How  much  change  should  a  lady  receive 
after  paying  for  the  oranges  with  a  two-dollar  bill  ? 

7.  Make  a  problem  with :  $  8.25,  $  6.32,  $  6.56,  and 
$5. 

8.  John  paid  a  bill  of  $  7.32  and  had  $  6.54  remain- 
ing.    How  much  had  he  at  first  ? 

9.  If  there  are  28  lines  on  each  page  of  a  book,  how 
many  lines  are  there  on  9  pages  ? 

10.  A  furniture  dealer  paid   $624  for  tables  at   $6 
each.     How  many  did  he  buy  ? 

11.  Jack  has  collected  250  post  cards  and  pastes  5  on 
each  page  of  his  album.     How  many  pages  do  they  fill  ? 

12.  How  many  lamps,  at  $  5  each,  can  be  bought  for 
$  83  ?     How  much  money  will  remain  ? 


Oral  and  Written]  ADDITION  63 

DRILLS  IN  ADDITION 

Add  rapidly,  finding  3  answers  in  1  minute. 


a 

b 

C 

d 

e 

1.  2345 

3256 

3556 

4325 

2546 

3253 

5433 

5234 

2534 

3452 

1432 

2345 

3245 

3523 

2543 

2564 

4356 

5243 

2456 

3245 

7316 

5134 

2356 

5346 

1236 

2.  2434 

3245 

2546 

6513 

5342 

3256 

1452 

4532 

3245 

4254 

5145 

5416 

3251 

5314 

6143 

4253 

2533 

5424 

2425 

3325 

3242 

3254 

1243 

5253 

2543 

3.  6325 

6436 

6323 

6546 

6546 

4264 

2462 

2566 

3562 

4362 

2633 

6354 

6344 

6255 

6543 

•  1462 

5633 

2565 

5364 

2544 

6326 

3265 

6355 

4534 

6355 

4.  Give  sums  at  sight, 

thus:  32  +  40=72;  72  +  5=77, 

32  +  45 

55  +  34 

54  +  32 

26  +  34 

43  +  44 

64  +  36 

56  +  56 

23  +  34 

42  +  64 

25  +  56 

56  +  45 

64  +  46 

42  +  32 

36  +  25 

66  +  36 

64  +  35 

36  +  25 

26  +  43 

53  +  36 

54  +  26 

38  +  17 

37  +  26 

59+17 

35  +  45 

25  +  28:. 

29  +  16 

25  +  47 

57  +  24 

66  +  26 

38  +  26 

19  +  28      49  +  26      39  +  58      47  +  47      29  +  25. 


64  THIRD  YEAR  [Written 

SUBTRACTION 

From  804  take  365. 

1.  We  cannot  take  5  ones  from  4  ones. 

7    9  14         We  cannot  take  6  tens  from  0  tens. 
^  ^  ^         Take  1  hundred  from  8  hundreds ;  this 
^  ^  ^     leaves  7  hundreds.     1  hundred  equals  10 
^  ^  9     tens.     Take  1  ten  from  10  tens,  leaving 
9  tens.     1   ten  and  4  ones  are  14  ones. 
804  therefore  is  equal  to  7  hundreds,  9  tens,  and  14 
ones.     Subtracting,  the  difference  is  439. 


Subtract : 
a 

2.  6304 
3168 

b 

7065 
1474 

c 

6401 
3162 

d 

8014 
6202 

e 
4706 
2165 

3.  4060 

2976 

8305 
6012 

8560 
3574 

6070 
4304 

4904 
1060 

4.  6105 
2166 

7805 
4991 

6099 
4814 

3940 

2108 

6303 
1494 

5.  8110 

4884 

4444 
2666 

6222 

4879 

8314 
6070 

8196 
7246 

6.  6162 
3104 

3110 
2904 

5641 
3212 

4132 
1841 

6112 

3897 

7.    Find   the    difference   between    8904   and    1996; 
between  9630  and   2709. 


Written]                         SUBTEACTION  65 

DRILLS    IN   SUBTRACTION 

Subtract,  finding  5  remainders  in  1  minute: 

a                    b                     c                    d  e 

1.  5434    3254    4203    6043  2015 
3565    2435    1564    2564  1356 

2.  4360     3204     3204     2010  3014 
2654     1605     1316     1516  2546 

3.  3105     4010     6302     3051  6031 
1046    2505    2603    2103  5076 


I 


4.  6035    6501    1045    3060    4320 
2456    2436     556    2065    1556 


2601 

3561 

6306 

1654 

1456 

2501 

2041 

6020 

5031 

1554 

1615 

1025 

3014 

2031 

6072 

2245 

1505 

4003 

6203 

4106 

2435 

5204 

3502 

1543 

5.  1405  2601  3561  6306  5041 

656  1654  1456  2501  1305 

6.  6702  2041  6020  5031  6043 
3026  1554  1615  1025  1245 


7.  6103  3014  2031  6072  5102 
2005  2245  1505  4003  3248 

8.  5203  6203  4106  2435  5210 
1546  5204  3502  1543  1435 


66  THIRD  YEAR  [Written 

DRILLS   IN   MULTIPLICATION   AND   DIVISION 

Multiply  and  divide  each  number  by  2,  3,  4,  and  5 : 


a 

b 

c 

a 

e 

/ 

1.  468 

456 

273 

332 

634 

804 

2.  684 

654 

372 

233 

436 

972 

3.  236 

564 

732 

548 

364 

729 

4.  632 

542 

412 

485 

184 

908 

5.  846 

452 

214 

854 

418 

890 

Multiply 

and  divide  each  number  by  6, 

5,  4,  and  3  : 

6.  426 

848 

408 

798 

249 

284 

7.  264 

844 

840 

897 

942 

428 

8.  624 

853 

480 

789 

429 

842 

9:  165 

790 

981 

679 

257 

912 

10.  561 

970 

189 

796 

725 

192 

Multiply 

and  divide  each  number  by  2, 

4,6,i 

md  5: 

11.  456 

295 

217 

513 

665 

537 

12.  654 

925 

172 

135 

656 

357 

13.  546 

529 

918 

150 

250 

640 

14.  237 

592 

189 

510 

520 

460 

15.  372 

712 

891 

566 

502 

604 

Multiply  and  divide  each  number  by  3,  5,  6,  and  4 : 

16.  206  666         270         474         228  924 

17.  620  246  720         276         282         492 

18.  457  426         372         822         249         742 

19.  475  642         723         726         846  952 


Oral]  MEASURES  67 

DRY  MEASURES 

1.  Name  some  dry  articles  purchased  by  the  pint ;  by 
the  quart ;  the  peck ;  the  bushel. 

2.  Secure  some  sand  or  grain,  and  show  by  actual 
measurements  the  number  of  pints  in  a  quart ;  the  num- 
ber of  quarts  in  a  peck ;  the  number  of  pecks  in  a 
bushel. 

3.  Memorize  this  table  : 


2  pints  =  1  quart ;  written,  2  pt.  =  1  qt. 
8  quarts  =  1  peck ;  written,  8  qt.  =  1  pk. 
4  pecks  =  1  bushel ;   written,  4  pk.  =  1  bu. 


4.  1  bu.  =  pecks ;  1  pk.  =  — —  quarts. 

5.  How  many  quarts  equal  1  bushel  ? 

6.  J  pk.  =  quarts  ;  |^  pk.  =  quarts. 

7.  At  10^  per  quart,  find  the  cost  of  8  quarts  of 
cherries. 

8.  At  6^  per  quart,  find  the  cost  of  1  peck  of  hazel- 
nuts. 

9.  A   horse   eats   12   quarts  of    oats  a  day.      How 
many  quarts  does  it  eat  in  4  days  ? 

10.  21  pk.  = quarts  ;  16  qt.  = pecks. 

11.  James    bought    1^    bushels    of    tomatoes.      How 
many  pecks  did  he  buy  ? 

12.  If  I  buy  I  peck  of  cherries,  how  many  quarts, 
should  I  get? 


68  '  THIED  YEAE  [Oral  and  Written 

LIQUID   MEASURES 

1.  Name  some  liquids  sold  by  the  pint ;  by  the  quart ; 
the  gallon. 

2.  Memorize  this  table  : 


2  pints  =  1  quart ;  written,  2  pt.  =  1  qt. 
4  quarts  =  1  gallon  ;  written,  4  qt.  =  1  gal. 


3.  2  gallons  =  how  many  quarts  ? 

4.  From  a  gallon  of  milk  how  many  quarts  could  be 
sold  ?  how  many  pints  ? 

5.  Mrs.  Adams  buys  2  quarts  of  milk  per  day.  How 
many  quarts  does  she  buy  in  20  days  ?  how  many 
gallons  ? 

6.  At  6^  per  quart,  how  much  does  the  milk  cost 
her  per  week  ? 

7.  From  a  cask  containing  3  gallons  of  vinegar,  how 
many  quarts  could  be  sold  ? 

8.  How  many  pints  are  there  in  12  quarts?  how 
many  gallons  ? 

Copy  these  problems  and  insert  the  answers  in  the 
blank  spaces : 

9.  1  qt.  =  pt.  14.    4  gal.  =  qt. 

10.  8  qt.  =  gal.  15.    24  qt.  =  gal. 

11.  16  pt.  =  qt.  16.    6  pt.  =    qt. 

12.  8  gal.  =  pt.  17.    4  qt.  =  gal. 

13.  8  pt.  =  qt.  18.    5  gal.  =  pt. 


Oral] 


MEASURES 


I 


MEASURES   OF   WEIGHT 

1.    Tell  how  the  following  articles  are  sold  : 
Butter,  eggs,  milk,  cheese,  coal,  oil. 

2.   Give  the  tables  of 


liquid  measures  and  dry 
measures. 

The  smallest  weight 
in  the  picture  is  called 
an  ounce  weight.  The 
largest  weight  is  a  six- 
teen-ounce  weight,  and 
is  called  a  pound  weight. 

Any  article  that  the 
pound  weight  balances 
is  said  to  weigh  just  one 
pound. 


16  ounces  =  1  pound ;   written,  16  oz.  =  1  lb. 


3.  A  lady's  purchase  at  the  store  is  balanced  by  the 
8  oz.  weight.     What  is  the  weight  of  her  package  ? 

4.  6  oz.  +  4  oz.  4-  6  oz.  = lb. 

5.  10  oz.-fl2  oz.  +  lO  oz.  = lb. 

6.  Jlb.  = oz.      ilb.  =  — oz.     |-lb.  = oz. 


70  THIRD   YEAR  [Oral 

MEASURES   OF   LENGTH  OR  DISTANCE 

1.  Examine  a  foot  rule. 

2.  Into  how  many  parts  do  the  long  marks  divide 
the  rule  ? 

3.  The  distance  between  any  two  of  these  marks  is 
called  one  inch. 

4.  Count  the  inches  in  a  foot. 

5.  Place  the  rule  on  a  paper  or  on  the  blackboard 
and  mark  oft'  a  line  12  inches  long. 

6.  A  line  12  inches  long  is  called  one  foot. 


12  inches  =  1  foot ;   written,  12  in.  =  1  ft. 


7.  Short  distances  are  measured  in  inches  ov  feet, 

8.  6  inches  is  what  part  of  a  foot  ? 

9.  Draw  a  line  J  ft.  in  length.     How  many  inches 
long  is  the  line  ? 

10.  Draw  a  line  J  ft.  in  length.  How  many  inches 
long  is  this  line  ? 

11.  Without  the  aid  of  a  rule,  draw  a  line  12  inches 
in  length ;  6  inches  in  length ;  2  feet  in  length. 

12.  Place  the  rule  on  the  lines  in  problem  11  and 
observe  how  much  too  long  or  too  short  they  were 
drawn. 

Pupils  should  practice  this  kind  of  work  until  they  can  esti- 
mate length  quite  accurately. 


Oral  and  Written]  MEASURES  73 


MEASURES  OF  LENGTH  OR  DISTANCE 

1.  Measure  the  top  of  your  desk  in  feet  and  inches. 

2.  J  ft.  = inches ;  J  ft.  = inches. 

3.  Some  articles  are  sold  by  a  measure  3  times  the 
length  of  a  foot  rule.     Name  some  of  them. 

4.  Draw  a  line  on  the  blackboard  3  feet  in  length. 

5.  The  line  you  have  drawn  is  one  yard  long. 


3  feet  =  1  yard ;  written,  3  ft.  =  1  yd. 


6.  A  piece  of  cloth  is  6  yards  long.     How  many 

feet  is  it  in  length  ? 

Copy  and  fill  in  the  blanks : 

7.  36in.  = ft.  13.    4     ft.  = in. 

8.  3ft.  = yd.  14.    21  ft.  = in. 

9.  2  ft.  = in.  15.    31  yd.  = ft. 

10.  60in.  = ft.  16.    15  ft.  = yd. 

11.  18ft.  = yd.  17.    7    yd.  = ft. 

12.  3  ft.  = in.  18.    6     ft.  = in. 

Change : 

19.  2  ft.  and  3  in.  to  inches.  25.    36  in.  to  yards. 

20.  3  ft.  and  4  in.  to  inches.  26.    12  ft.  to  yards. 

21.  4  yd.  and  1  ft.  to  feet.  27.    24  in.  to  feet. 

22.  6  yd.  and  2  ft.  to  feet.  28.  48  in.  to  feet. 

23.  27  in.  to  feet  and  inches.  29.    36  yd.  to  feet. 

24.  16  ft.  to  yards  and  feet.  30.  5^  yd.  to  feet. 


72  THIRD   YEAR  [Oral  and  Written 

READING   AND   WRITING    NUMBERS 

In  reading  large  numbers,  separate  them  by  commas 
into  groups  of  three  figures  each,  beginning  at  the  right. 

Each  group  is  called  a  period  and  has  ones  place, 
tens^  place,  and  hundreds'  place.  The  last  period  to  the 
left  may  contain  only  one  or  two  figures ;  as,  8,245 ; 
28,375. 

Beginning  at  the  right,  the  places  in  24,205  are  called 
ones^  tens,  hundreds,  thousands,  tens  of  thousands.  The 
number  is  read,  ''  24  thousand,  205." 

Copy,  point  off  into  periods,  and  read : 

abed 

1.  45268      65283      25834      31849 

2.  39371      94736      93687      40306 

3.  20905      18110      60009      37000 

ROMAN  NUMERALS 

1.  Write  the  Roman  numerals  from  11  to  19.  Place 
X  before  each.     This  gives  the  numerals  from  21  to  29. 

2.  XXX  -  30.     L  =  50.     XL  =  40. 

Write  the  numerals  from  31  to  40  ;  from  41  to  50. 

3.  LX  =  60.     LXX  =  70.     LXXX  =  80. 
Write  the  numerals  from  50  to  70. 

4.  C  =  100.     CC  =  200.     XC  =  90.     XCIX  =  99. 
Write  the  numerals  from  70  to  100. 

Write  210,  290,  299,  300,  349,  235,  341. 
Read  XCIT,  CIX,  CCXL,  CCXCIX 


Written]  UNITED  STATES  MONEY  73 

ADDITION  AND  SUBTRACTION  OF  U.  S.  MONEY 

Eead  and  add : 


a 

6 

e 

d 

$286.75 

$364.92 

$615.94 

$961.37 

931.49 

19.39 

293.29 

149.95 

86.72 

187.46 

89.67 

98.69 

73.87 

29.84 

173.28 

83.75 

68.45 

382.73 

8.75 

278.87 

$24.35 

$15.46 

$21.95 

$43.74 

13.64 

33.71 

15.84 

17.27 

71.25 

16.15 

22.65 

33.75 

45.32 

32.43 

16.34 

45.45 

3.  $  8692  +  $  193.75  +  $  475.86  +  $  286.37  +  $  90 

4.  $  187.14  +  %  275.61  +  $  630.18  +  $  5.25  +  $  0.18 

5.  $  263.35  +  $  436.75+  $  195.19  +  $  2.75  +  $  84 


Subtract : 

a 

h 

c 

d                e 

6.    $243.56 

$315.46 

$254.73 

$269.46    $226.42 

186.38 

169.75 

80.06 

178.95          9.70 

7.  $486  35     $268.43     $124.39    $923.14    $275.86 

129.76       174.85         86.41       189.67      185.86 

Find  the  difference  between  : 

8.  $406.75  and  $216.40     ii.  $436.74  and  $175.12 

9.  $325.43  and  $   74.65     12.  $263.37  and  $144.00 
10.    $468.36  and  $196.09     13.  $276.10  and  $186.19 


74  THIED   YEAR  [Oral  and  Written 

HALVES 

1.  Into  how  many  parts  has  the  circle 
been  divided  ?  What  is  the  name  of  each 
part  ?  Into  how  many  halves  can  an  ob- 
ject be  divided  ? 

2.  1  half  apple +  1  half  apple  =  ?  $1  +  $|  =  ? 

3.  1  half  dozen  + 1  half  dozen  =  ?         ^  yd.  +  ^  yd.  =  ? 
Find  the  sum  of : 


4.    11  gal. 
3  gal. 

5. 

41  bu. 
21  bu. 

6.     51 

yd.         7. 

yd. 

3Jqt- 
*qt. 

8.  Add: 

15^    i  +  i  =  l;  1  +  |  =  1|. 

9J         Write  the  fraction 

6J    numbers. 
31J 

• 
J,  and  add  1  to  the  whole 

9.    41  +  271 

+  H 

11. 

111  +  251 

+  421 

10.   91 +  181 

+  27| 

12. 

9    +371 

+  86^ 

Insert  the  missing 

13.    ^     n 

+      + 

number : 

+ 

8* 
+ 

9* 

+ 

11 

+ 

101 

l^ 

n 

12* 

18* 

201 

Subtract : 
14.         81 

-5 

-3 

12* 
-10* 

11* 

-  n 

14* 

-   7* 

16* 

-   8* 

15.      241 

-   71    - 

17i 

^ 

251 
-18* 

38* 

-251 

621 
-37 

49| 
-261 

Oral  and  Written] 


FRACTIONS 


u 


'/3 

'/3 

•/3 

THIRDS 

1.  How  many  thirds  are  there  in 
the  oblong?  How  many  thirds  are 
there  in  one  of  anything  ?  in  1  yard  ? 
How  many  feet  are  there  in  1  yard  ?  What  part  of  a 
yard  is  1  foot  ?  What  part  of  a  yard  is  12  inches  ? 
How  many  thirds  are  there  in  2  oranges  ? 

Add: 

2.  i+i  =  i     J  +  l  +  i=iorl     |-|-|  +  |  =  |,or2 

a  h  c  d  e 

3.  '" 


5. 


4* 

61 

5i 

8J 

9* 

+  21 

+  li 

+  4 

+  5* 

+  11 

8J 

7f 

9* 

7 

12 

10* 

H 

5 

8| 

8* 

121 

M 

M 

6i 

9| 

id  the 

missing  number 

: 

^ 

% 

7 

15J 

8f 

+ 

+ 

+ 

+ 

+ 

111 

14f 

12| 

18| 

lit 

7* 

8§ 

9f 

18f 

17| 

-3 

-5^         . 

-4f 

-   5| 

-9| 

7.   I  rubbed  out  2|  inches  from  a  line  5f  inches  long. 
How  long  was  the  part  remaining  ? 


76 


THIRD  YEAR  [Oral  and  Written 


FOURTHS 

1.  Into  how  many  parts  has  the 
square  been  divided?  Give  the  name 
of  each  part.  What  is  the  difference 
between  a  quarter  and  a  fourth  of  $  1  ? 
of  1  pie  ?  of  1  apple  ?  Into  how  many 
fourths   can    any   object    be    divided  ? 

4+i  +  4=how  many  fourths  ?     f  gal.  -f  J  gal 

Find  the  sum  : 


'U 

'A 

'A 

y^ 

2.  $2i+$| 

4. 

6i 

gal.  +   1  gal.     6. 

81  bu.  +  f  bu. 

3.     61+     i 

5. 

H 

pk. +2|pk.      7 

7|hr.  +  li  hr. 

Add: 

a 

h 

c                A 

e             / 

8.      2i 

6i 

5i            3i 

lOf          121 

3f 

11 

6i            8i 

7f           9 

5i 

8f 

25i           9i 

8|           8| 

9.    11 

18f 

191             1 

h\         201 

141 

16f 

8                1 

6|            8 

271 

21| 

62f             1 

17            31| 

Complete : 

10.   41  +  ?=  9f 

12. 

6i  +  ?=lli 

14.  ?  +  8i  =  15i 

11.   6|+?=8| 

13. 

9i  +  ?=13f 

15.   ?+   1=    G| 

Find  the  difference : 

16.     81-7 

19.     9|-  SJ 

22.    19|-7i 

17.   16|-5i 

20.   161-   71 

23.     161-8 

18.   23f-7f 

21.    12|-11| 

24.     141-7 

Written]  PRACTICAL   PROBLEMS  77 

PRACTICAL   PROBLEMS 

1.  A  dealer  sold  2^  tons  of  coal  at  one  time  and  3 J 
tons  at  another  time.     How  many  tons  did  he  sell  ? 

2.  From  a  barrel  containing  31J  gallons,  25  gallons 
were  sold.     How  many  gallons  remained  ? 

3.  A  dairyman  sold  in  one  month  1875 J  gallons  of 
milk.  He  sold  250  gallons  less  the  next  month.  How 
much  did  he  sell  the  second  month  ? 

4.  A  farmer  picked  potatoes  as  follows :  23  bu., 
24ibu.,  and  111  bu.    How  many  bushels  did  he  pick? 

5.  After  selling  56^  bu.  of  the  potatoes,  how  many 
bushels  remained  ? 

6.  7f  yards  of  silk  were  cut  from  a  piece  containing 
18f  yards.     How  many  yards  remained  ? 

7.  A  dressmaker  used  5|  yards  of  cloth  for  a  skirt 
and  2|  yards  for  a  waist.  How  many  yards  did  she  use 
for  both  ? 

8.  Mr.  Miller  owned  301  acres  of  land.  He  kept  241 
acres  and  sold  the  remainder  at  $48  an  acre.  How 
much  did  he  receive  for  the  part  sold  ? 

9.  Find  the  weight  of  4  baskets  of  butter  contain- 
ing 351  lb.,  18  lb.,  221  lb.,  and  16  lb.,  respectively. 

10.  Harry  made  8 J  gallons  of  lemonade  and  sold  7 
gallons.     How  much  was  unsold  ? 

11.  Find  the  distance  around  a  room  that  is  18|  ft. 
long  and  16  ft.  wide. 


78  THIRD  YEAR  [Oral  and  Written 

REVIEW 

1.  Count  by  5's  from  0  to  100. 

2.  Count  by  6's  from  0  to  120. 

The  sign  @  followed  by  a  price  means  "  at "  so  much 
a  unit.  ThuSj  "  3  lb.  steak  @  15  ^  "  means  "  3  lb.  steak 
at  15^  a  pound;''  "6  doz.  buttons  @  20^"  means 
"6  doz.  buttons  at  20^  a  dozens 

Find  the  amount  of  each  of  the  following : 

3.  3  lb.  steak  @  15^'. 

4.  6  bu.  potatoes  @  48  ^. 

5.  6  lb.  sugar  @  4  ^. 

6.  5  cans  tomatoes  @  12^. 

7.  6  doz.  eggs  @  22^. 
Find  the  cost  of : 

8.  5  sheep  @  $  4.75.  i3.    6  hats  @  $1.25. 

9.  6  bureaus  @  $7.75.         14.   5  books  @  $  1.75. 

10.  6  cows  @  $48.  15.    6  lamps®  $1.33. 

11.  6  rugs®  $4.75.  16.   6  wagons  ®  $85. 

12.  5  vases  ®  $2.65.  i7.   5  horses  ®  $  175. 

18.  Add  45  and  56,  thus :  45  and  50  are  95 ;  95  and 
6  are  101. 

Add  in  the  same  way : 

19.  35  and  48    23.  78  and  64  27.  19  and  96 

20.  18  and  25    24.  84  and  76  28.  78  and  97 

21.  20  and  46    25.  93  and  42  29.  87  and  46 

22.  81  and  72    26.  48  and  75  30.  96  and  41 


Oral  and  Written]      MULTIPLICATION 


79 


MULTIPLYING    BY   7 

1.  Count  by  7's  to  21 ;  to  42  ;  to  63  ;  to  84. 

2.  2x7  =  ?  3x7  =  ?  etc.,  to  12  x  7  =  ? 

3.  Build  the  table  of  7's.  3^-^ 

4.  Compare    in    value    5x7    and     ^y  ^^ 
7x5;     3x7    and    7x3;    7x6    and    J        7^.        |5 
6x7;  7  X  2  and  2  X  7;  4  x  7  and  7  x  4, 

Table  of  7's 


8" ^ 


1x7=   7 

7x7  =  49 

2x7  =  14 

8x7  =  56 

3x7  =  21 

9x7  =  63 

4x7  =  28 

10x7  =  70 

5  X  7  =  35 

11x7  =  77 

6x7  =  42 

12x7  =  84 

5.  Memorize  the  table. 

6.  What      multiplicand 
and  multiplier  make: 

49  12  36  28  24 

35  30  14  18  14 

25  42  20  27  21 

63  84  77  72  54 


a 
2456 
x7 

7739 
x7 


h 
3265 
x7 

8497 
x7 


C 

4157 
x7 

6198 

X  7 


d 

8963 
x7 

5424 
x7 


« 
9045 
x7 

6339 

X  7 


Multiply  by  7,  testing  answers : 
9.   4693  7528  6934  8576  7935 

10.   7208  5697  2469  3875-         8094 


80 


THIRD  YEAR  [Oral  and  Written 


MULTIPLYING   BY  8 

1.  Count  by  8's  to  24 ;  to  64  ;  to  96. 

2.  How  many  are  2x8  balls  ?    3  x  8  books  ?    4x8 

4  boys  ?    5x8  pens  ?    6x8  apples  ? 

^"""^^         3.   Build  the  table  of  8's. 
12/  V        4.    Give  quickly: 


'"^        /     6x    8 

8x    6        7x8        5x   8 

yii     8x    4 

8x10         8x2         8x11 

-^        8x12 

4x   8         6x8         8x    5 

Table  of  8's 

5.   Memorize  the  table. 

1x8=    8 

7x8  =  56 

2x8  =  16 

8x8  =  64 

3x8  =  24 

9x8=72 

4x8  =  32 

10x8  =  80 

5x8  =  40 

11x8  =  88 

6x8  =  48 

12x8  =  96 

a 

7.  6230 

8.  2937 

9.  9048 


b 
5178 
8694 
6937 


6.    Give  answers: 


?x8  =  32 

6x  ?  =  48 

?x8  =  72 
lOx  ?  =  80 
12x  ?  =  96 

Multiply  by  8 

c  d 

8629  9310 

9083  8697 

2865  4705 


7x  ?  =  56 
?x5  =  40 
8x  ?=64 
?x3  =  27 
2x  ?=18 


e 

7865 
7289 
8136 


Give  products  at  sight : 

10.  8x50        8x70  8x91  8x12  8x31 

11.  7x40        7x60  7x71  8x11  7x20 

12.  8x90        7x81  8x30  7x21  8x61 


Written] 


MULTIPLICATION 


81 


PRACTICAL  PROBLEMS 


1 

I    HBBBBB 

BBBHBB 

,    BBBBBB    J 
•    BBBBBB    ' 

BBBBBB 

BBBBBB 
BBBBBB 

BBBBBB 
^—. fl 

1.  This  schoolroom  is  32 
feet  long  and  28  feet  wide'. 
What  is  the  distance  around 
it? 

2.  The  glass  in  each  win- 
dow cost  $2.50.  How  much 
was  paid  for  all  the  glass  ? 

3.  Each  desk  cost  $3.25. 
Find  the  cost  of  the  desks 
in  each  long  row. 

4.  Find  the  value  of  the  desks  in  the  6  rows. 

5.  The  attendance  for  the  first  8  school  days  was  as 
follows:  36,  43,  42,  43,  37,  41,  43,  43,  respectively. 
What  was  the  average  attendance  ? 

Note.  —  To  find  the  average  add  the  eight  numbers  and  divide 
the  sum  by  8. 

6.  Eight  tons  of  coal  were  used  during  the  term. 
How  much  w^as  paid  for  the  coal  at  $  4.50  a  ton  ? 

7.  What  is  the  amount  of  the  teacher's  salary  for  8 
months,  at  $  50  a  month  ? 

8.  Find  the  entire  cost  of : 

8  Advanced  Geographies  at  $1.00  each. 
8  Primary  Geographies  at  $  .45  each. 
8  Grammars  at  $  .50  each. 
8  Language  Lessons  at  $  .35  each. 
8  Readers  at  $  .48  each. 


82 


TPIIRD  YEAR  [Oral  and  Written 


DIVIDING   BY   7 

1.  How  many  times  is  7  contained  in  14?     in  21? 
42?    63?   28?    35?    49?    70?    77?    56? 

2.  Find!  of  84;  63;  42;  35;  56;  70;  14;  21. 

Divide : 

a  b  c  d  e  f 

3.  7H2        7)63        7)56        7)49         7)84        7)35 


4.  6)72   5)45 

6)42 

7)28 

6)48 

7)70 

Divide  by  7 : 

5.   84     56 

59 

68 

45 

36 

6.  217    364 

427 

637 

273 

696 

Divide  and  test : 

7.    7)2436       6)7391       7)8693       6)7857       7)4693 
a   5)2609       7)8054       6)3079       7)2096       5)8097 


9.    7)7381       6)2867       7)2536       5)3204       7)6973 

10.  How   many  7-pound  boxes    can   be    filled   from 
259  pounds  of  barley  ? 

11.  How  many  weeks  are  there  in  49  days  ? 

12.  How  many  suits,  each  requiring  7  yards,  can  be 
made  from  a  piece  of  cloth  containing  84  yards  ? 

13.  How  many  7^  packages  of  crackers  can  be  bought 
for  $  1,  and  how  much  money  will  be  left  ? 


Oral  and  Written] 


DIVISION 


83 


1.  48-8-8-8 

2.  2x8  =  ?   16 

3.  32^8  =  ?  40 

4.  64  contains  8,  — 
56  contains  8,  — 
96  contains  8, — 

Give  quotients : 
a  b 

5.  8]64  8}32 

6.  8U6 

7.  7)_35 

Find: 

8.  1  of  72 

9.  1  of  640 


DIVIDING   BY  8 

8-8=?  48-^6  =  ? 

2  =  ?    8x3  =  ?   24-^8  =  ?    8x4  =  ? 

5  =  ?  56-^8  =  ?   64^8  =  ?  72-^8  =  ? 


times 
times 
times 


72  contains  8, 
48  contains  8, 
88  contains  8, 


7)_56_ 
8)88 

lof  64 
1  of  720 


c  d 

8}40  8)72 

8)24  7)63 

7)28  8)_96 


1  of  32      1  of  56      1  of  48 
1  of  400     i  of  320     J  of  800 


times 
times 
times 

e 

8)56 

8)48 

8)80 


Divide  by  8: 

10.  175  823  629  473  621 

11.  8073  2096  3075  4083  6029 

12.  2903  8107  2904  7908  8604 

13.  6195  2936  8629  4175  2936 

14.  Hov^^  many  tablets  at  8^  each  can  be  bought  for 
$  1,  and  how^  many  cents  will  be  left  ? 

15.  A  furniture  dealer  paid  $  240  for  ice  chests  at 
$  8  each.     How  many  chests  did  he  purchase  ? 


84 


THIRD   YEAR 


[Written 


MULTIPLICATION   BY  MIXED   NUMBERS 

A  mixed  number  is  composed   of  an  integer  and  a 
fraction. 

1.   Multiply  16  by  2i. 

16 


2i 


lofl6=    8 
2  xl6  =  32 


2 J  times  16  means  that 
i  of  16  is  to  be  added  to 


21x16  =  40 


Find  products : 

2. 


-tt:  2  times  16. 


3. 
4. 
5. 
6. 
7. 


21x24 
21x36 
41 X  96 
81x84 
6|  X  60 
81x120 


8. 

9. 
10. 
11. 
12. 
13. 


71x336 
81 X  124 
91 X  276 
71 X  324 
51 X  288 
7^x240 


Shout  Form 

16 

t 

2i 
8 

3 

32 
40 

14. 

81 X 

273 

15. 

61 X 

258 

16. 

8ix 

744 

17. 

91 X 

275 

18. 

51 X 

392 

19. 

9^x 

413 

Find  the  cost  of: 

20.  8|-  gal.  oil  @  12^.  27. 

.21.  6|-  bu.  potatoes  @  80)^.  28. 

22.  81  yd.  silk  @  $  1.20.  29. 

23.  7 1  gal.  milk  @  16^.  30. 

24.  6;^  doz.  bananas  @  24^.  31. 

25.  61  doz.  buttons  @  54  j^.  32. 

26.  7 J  yd.  ribbon  @  28^,  33. 


71  doz.  buttons  @36^. 
9-J-  hours'  work  @  18^. 
8  J  pounds  butter  @  32  ^. 
6^  pounds  meat®  16^. 
7^  pk.  peaches  @  40^. 
3|-  yd.  muslin  @  16^. 
411b.  candy  @  60^. 


Oral  and  Written]      MULTIPLICATION 


85 


MULTIPLYING  BY  9 

1.  Count  by  9's  to  27 ;  to  54 ;  to  72 ;  to  108. 

2.  Build  the  table  of  9's. 

3.  Compare  6x9  and  9x6;  8x9  and  9x8;  10  x  9 


and  9  X  10. 

4.    Multiply  at  sight  by  9  : 
40     60     80     20     50     10     30 


Table  of  p's 

1x9=   9 

7x9=    63 

2x9  =  18 

8x9=   72 

3x9  =  27 

9x9=   81 

4x9  =  36 

10x9=    90 

5  X  9  =  45 

11x9=    99 

6  X  9  =  54 

12x9  =  108 

70    90    31     51     71 

Memorize  the  table. 


Give  two  numbers  that  form  each  of  these  products : 

6.  21,  36,  44,  48,  50,  40,  54,  45,  33,  18,  27,  99. 

7.  88,  90,  60,  77,  81,  63,  66,  72,  56,  108,  96,  80. 
Multiply  by  9 : 

a                    b  c                    d                    e 

8.  4693    7286  4615     8738     6957 

9.  4135    2874  6398     1869     7043 

10.  8286    3697  4589     2893     9097 

11.  9387    2945  9384     9387     2864 

12.  6005    7894  5009     6090     7500 

13.  5020    4080  3074     8005     9999 


86 

THIED  YEAR 

[Oral  and  Writtea 

MULTIPLYING  BY 

9 

Multiply  by 
a 
1.    4226 

9: 

b 
8393 

c 
3786 

a 

2468 

e 
8321 

2.    5483 

6692 

2294 

8329 

6245 

3.    6396 

2594 

4968 

5692 

9374 

4.    7278 

7246 

5328 

7386 

8928 

Find  the  products: 
5.  9  X  38  gal.   9  X  24  da.     9  x  16  min. 
II  6.  9  X  17  bu.    9  X  25  mo.    9  x  25  horses 

7.  9x12  ft.     9x18^        9x35  cows 

8.  Find  products  by  7  ;  by  8 ;  by  6. 

Table  of  Elementary  Products 

In  multiplication,  there  are  45  different  combinations 
of  figures  taken  two  at  a  time,  and  36  different  prod- 
ucts.    Use  these  combinations  for  drill  frequently : 


1 

1 

1 

2 

1 

1 

3 

1 

1 

4 

1     , 

1 

2 

3 

2 

4 

5 

2 

6 

7 

2 

8 

3 

1 

5 

6 

4 

7 

5 

,4 

8 

9 

6 

3 

9 

2 

2 

3 

2 

3 

4 

2 

2 

3 

5 

7 

8 

6 

5 

9 

7 

6 

8 

7 

6 

4 

3 

3 

4 

5 

3 

4 

5 

4 

5 

6 

9 

8 

7 

9 

8 

7      9 

8 

9 

8 

9 

9 

4 

5 

6 

5 

6 

7      6 

7 

7 

8 

8 

9 

Oral  and  Written]  DIVISION  87 

DIVIDING   BY   9 

1.  How  many  tables,  at  $9  each,  can  be  bought  for 
$18?  for  $27?  for  $36?  for  $45?  for  $63? 

2.  Give  quotients  at  sight : 


63  H- 9 

81^9 

45^5 

36^4 

108^9 

72^8 

54H-6 

72-4-9 

27^8 

90^9 

lof  36 

^of  63 

lof  54 

iof  56 

ioi  72 

J  of  64 

iof45 

^of45 

lof  63 

|of  56 

3.   Tell  at  sight  which  is  greater  and  how  much: 
1  of  81  or  1  of  27  I  of  40  or  i  of  45 

1  of  64  or  1  of  16  1  of  63  or  i  of  81 

Divide  by  9  ;  then  by  8  : 

a                      b                        c                      d  e 

4.  2637     1856     2934  7683  8174 

5.  6385     2097     3084  6075  7238 

6.  8462     3761     2985  2207  3604 

7.  7581     6293     8697  2984  6093 

8.  Give  quotients  at  sight : 

180-^-9         360^9         900-^9         720-^9         729-^9 
279^9         549^9         459^9         639^9         450^9 

9.  If  a  postman  delivers  954  letters  in  9  hours,  how 
many  letters  does  he  average  in  one  hour  ? 

10.  How  many  times  can   9   inches  be  marked  o£E 
from  a  line  4J  feet  in  length  ? 

11.  At  3  melons  for  15  cents,  how  many  melons  can 
I  buy  for  45  cents  ? 


88  .  THIRD  YEAR  [Written 

DIVISION   OF   DOLLARS   AND   CENTS 

Find  the  products ;  test  and  read  answers : 

a  b  c 

1.  4  X  $2.75  7  X  $82.93  8  x  $93.15 

2.  5  X  $3.86  8  X  $46.25  9  x  $73.86 

3.  6  X  $7.27  9  X  $73.87  7  x  $49.25 

4.  Divide  $6.15  by  3. 

Divide  $  6.15  by  3,  placing   a  decimal 
3)$  6.15    point  under  tlie  decimal  point  in  the  divi- 
$2.05     dend.     Write  the  dollar  sign  before   the 
number  of  dollars  in  the  quotient. 

Find  the  quotients ,  read  and  test  answers : 


a 

5-   $4.75-^2 

b 

$6.75  +  4 

c 
$29.34  +  9 

6.  12.08  +  2 

7.  $9.27  +  3 
Find: 

$8.22  +  6 
$9.05  +  5 

$46.72  +  8 
$71.05  +  7 

a  J  of  $27.15            i  of  $16.64 
9.   |of  $18.24             ^of  $26.70 
10.  iof  $20.48             lof  $38.40 
Perform  the  operation  indicated: 

1  of  $39.34 
J  of  $97.68 
lof  $27.36 

11.    $273.84  +  6 

$263.75  +  8 

$375.42  +  6 

12.   $936.25x5 

$423.96x9 

$495.67  +  7 

13.    $475.83x6 

$928.14  +  6 

$321.21  +  9 

14.    $721.98  +  9 

$743.68  +  7 

$563.94x8 

15.    $435.72  +  8 

$269.19  +  9 

$732.75x6 

Written]        MULTIPLICATION  AND"  DIVISION 


89 


PRACTICAL   PROBLEMS 


1.  It  requires  4  yd.  of 
material  to  make  each 
of  these  girls  an  apron. 
How  much  will  be  re- 
quired for  the  class  of  7 
girls  ? 

2.  At  8^  a  yd.,  how 
much  will  7  aprons  cost  ? 

3.  Out  of  91  yd.  of 
cambric,  how  many  caps, 
requiring  ^  yd.  each,  can 
be  made  ? 

4.  How  many  pupils 
can  be  supplied  with 
rolling  pins  and  pie  pans 

out  of  $  9,  if  each  pin  costs  20^,  and  each  pan  10^? 

5.  At  18^  a  yard,  find  the  cost  of  lawn  for  sleeve 
protectors  for  7  girls,  each  sleeve  requiring  |  yd. 

6.  Miss  Blew,  the  teacher,  purchases  the  following : 
7  flour  cans  @  40^,  7  cake  pans  @  25^,  7  sugar  shakers 
@  17^.     Find  the  amount  of  her  purchases. 

7.  Entertaining  the  directors,  this  class  uses  7  spring 
chickens  @  40^,  2  pecks  of  potatoes  @  15^,  1  head 
cabbage  @  8^,  2  boxes  tomatoes  @  10^,  |-  lb.  butter  @ 
32^,  2  pt.  cream  @  8^,  and  J  gallon  ice  cream  @  $  1.50 
per  gallon.     How  much  does  the  dinner  cost  them  ? 


90  THIRD   YEAR  [Written 

MULTIPLICATION   AND  DIVISION 

Multiply  and  divide  by  8 ;  by  9  : 


a                    b 

c                    d                   e 

1.    2465           2469 

2816           6824           6178 

2.    7381          8397 

9375           4836          8293 

Find: 

3.   \  of  4687  sbeep     5. 

i  of  7353  bu.    7.  1  of  3600 

4.   i  of  9376  horses    6. 

i  of  4347  gal.    a  i  of  7479 

How  much   change   shall   I  receive  from    $10  for 

the  following  ?     Name  the' 

coins  in  each  purchase. 

9.   21  yd.  silk®  60^ 

11.    24  lb.  butter®  $J 

10.    7^  doz.  eggs  @  30^ 

12.   31  bu.  plums  @  $  2.50 

Market  Report 

Grapes,  per  crate,               $2.75 

Peaches,  per  basket,        $1..S5 

Blackberries,  per  crate,       |3.50 

Pears,  per  bbl.,                 $3.75 

Raspberries,  per  crate,        $3.65 

Apples,  per  bbl.,               $3.50 

Elderberries,  per  crate,       $1.75 

Cantaloupes,  per  box,      $4.50 

From  the  above  report  find  the  cost  of : 

13.  4  crates  of  blackberries.   20.    9  baskets  of  peaches. 

14.  5  baskets  of  peaches.       21.    6  crates  of  blackberries. 

15.  3  crates  of  grapes.  22.    5  crates  of  elderberries. 

16.  3  crates  of  elderberries.    23.    7  crates  of  raspberries. 

17.  4  bbl.  of  pears.  24.    6  bbl.  of  pears. 

18.  2  boxes  of  cantaloupes.   25.    8  boxes  of  cantaloupes. 

19.  6  bbl.  of  apples.  26.    8  baskets  of  peaches. 
Make  other  problems  from  this  or  another  Market 

Report. 


Written]  ADDITION  91 


UNITED   STATES   MONEY 

(Notice  the  groups  that  make  10  or  15.) 


Add: 


KX, 

6 

C 

d 

e 

515.73 

$30:861     $ 

6.93 

%      .48 

$     .17 

6.98 

15.29)'' 

32.63 

2.75 

.28 

.371 

8.88 

4.30 

.76 

5.70 

5.18  P" 

•^^Il5 

12.51 

5.85 

16.37 

40.60 

7.27 1 '' 

8.78 

40.20 

4.70 

5.891 

;■  1ft 

23.851 

\  1ft 

.36 

6.58 

23.96 

.31]'" 

.25  f"* 

.50 

18.64 

.85 

2.    Mr.  Foster  sold  in  5  days  as  follows.      Find  each 
day's  sales,  total  sales,  and  receipts  for  each  article. 


MON. 

Tubs. 

Wed. 

Thurs. 

FBI. 

a 

6 

C 

d 

e 

Corn 

$75.25 

$68.75 

$27.35 

$87.45 

$64.65 

Oats 

18.42 

26.73 

16.72 

29.63 

37.26 

Bran 

6.75 

3.75 

8.25 

7.75 

9.45 

Chop 

12.34 

8.65 

17.38 

15.24 

16.28 

Meal 

3.60 

5.40 

7.60 

12.60 

17.20 

Flour 

47.25 

68.25 

78.75 

89.25 

110.25 

3.  A  man  made  7  deposits  as  follows :  %  145.75, 
$123.34,  $  134.89,  $  645.75,  $  800.05,  $  900.25,  $845.52. 
How  much  money  did  he  deposit  ? 

4.  My  expenses  for  6  days  were  respectively,  $  1.42, 

$2.05,  $2.36,  $2.12,  $1.45,  and  $2.15.     What  were 
my  expenses  for  the  week  ? 


92 


1 
1 

THIRD  YEAR 

[Writtea 

SUBTRACTION 

1. 

From  5000  take  3456. 

• 

4  9  9  10 

6  from  10  leaves  4 

5000 

5  from  9  lea^ 

•es  4 

3456 

4  from  9  leaves  5 

1544 

3  from  4  leaves  1 

a 

6 

c 

d 

e 

2. 

6734 

8090 

7004 

6000 

9000 

4578 

5694 

5896 

4187 

3999 

2156 

2396 

1108 

1913 

5001 

Subtract : 

a 

h 

c 

d 

e 

3. 

9084 

7604 

5003 

8460 

6080 

6097 

4909 

3806 

7469 

5908 

4. 

9600 

7039 

6800 

7001 

4403 

3097 

6799 

5009 

1903 

3040 

5. 

5004 

8040 

7409 

6400 

7003 

3904 

4409 

3790 

4986 

6800 

6. 

8703 

6009 

8001 

5904 

9878 

5008 

4939 

6809 

3400 

4980 

7. 

7003 

5900 

9204 

7405 

5900 

4906 

3098 

8909 

6097 

4397 

Written]  REVIEW                                         93 

TEST    EXERCISES 

Multiply,  practicing  until  nine  products  can  be  found 
in  2  minutes. 

1.  4987  by  7  4.  2475  by  8  7.  6894  by  9 

2.  6879  by  8  5.  8689  by  9  a  9829  by  7 

3.  9836  by  9  6.  3978  by  7  9.  6375  by  8 

10.  8564  by  7  ^  13.  8739  by  9  le.  8795  by  9 

11.  9873  by  9  *  i4.  6927  by  8  17.  6938  by  7 

12.  8293  by  8  15.  8738  by  9  is.  9375  by  8 

19.  9365  by  8  22.  7693  by  7  25.  8756  by  9 

20.  8796  by  9  23.  8795  by  8  26.  7938  by  9 

21.  2493  by  7  24.  9283  by  9  27.  4695  by  7 

Add  rapidly : 

a  b                     c  d                      e 

28.  2401  2409     8145  3629     8873 

6375  3875     2693  9483     2345 

5816  4693     7856  2637     5690 

2487  9301     9037  3415     2295 

1789  1432     5009  8007     7986 


29. 


7895 

9982 

7743 

2239 

4498 

2398 

1028 

3838 

4075 

7659 

2015 

5690 

9723 

9320 

3376 

1920 

5497 

4587 

8756 

5072 

6099 

4705 

8243 

6008 

3490 

94 


THIKD   YEAR 


[Written 


PRACTICAL   PROBLEMS 


1.  The  drafting  room  is  24  feet  wide  and  28  feet 
long.     What  is  the  distance  around  the  room  ? 

2.  There  are  7  stands  in  the  room.  Each  one  cost 
$  5.50.     What  was  the  cost  of  all  ? 

3.  Each  stand  requires  a  "  T  "  square,  angles,  scale, 
erasers,  thumb-tacks,  etc.  The  instruments  cost  $  28.35. 
What  was  the  average  cost  of  each  stand  ? 

4.  The  first  class  worked  40  minutes  on  Monday 
and  Friday  of  each  school  week.  How  many  min- 
utes were  spent  by  the  class  during  4  school  weeks  ? 

5.  Each  of  7  boys  required  a  drafting  board  costing 
50^,  ink,  paper,  pencils,  etc.,  costing  25)^.  What  was 
the  cost  of  these  materials  for  the  class  ? 

6.  The  boys  made  two  chairs  valued  at  $  8.75  each, 
^3  tabourettes  at  $3.25  each,  and  4  book  racks  at 
$1.25  each.     What  was  the  value  of  all  the  articles? 


Written]                               EEVIEW  95 

TEST  EXERCISES 

Divide,  practicing  until  the  quotients  for  9  problems 
can  be  found  in  2  minutes: 

V   2873  by  7            4.   8196  by  8  7.   2403  by  9 

2.  9865  by  8             5.    7963  by  9  a   8173  by  8 

3.  4793  by  9             6.   8910  by  7  9.   6294  by  9 

10.  7386  by  8           13.   8197  by  8  16.   4003  by  8 

11.  8794  by  9           i4.   6934  by  9  17.   6920  by  7 

12.  9387  by  9           15.   7879  by  7  la   3784  by  9 

19.  9234  by  7           22.    6010  by  9  25.   3215  by  7 

20.  6875  by  8           23.   5362  by  7  26.   8629  by  9 

21.  4132  by  9           24.   8104  by  8  27.   9273  by  8 

Subtract  rapidly : 

2a  4284  -  2141      31.   8001  -  6448  34.   8004  -  2234 

29.  8401-1762      32.   6001-4999  35.   7982-5460 

30.  8109-4777     33.   9845-3677  36.   5698-3472 

37.   6024-5107     40.   9045-4254  43.   3498-2004 

3a    8460-6418      4i.   8700-4286  44.   6699-3342 

39.   7200-4540     42.   8760-4197  45.   7583-5620 

46.  8794-4587     49.   6001-2478  52.   5590-1056 

47.  8476-7421      50.   6424-3150  53.    9930  -  7810 
4a   8921-5879     51.   4030-3289  54.   9706-5897 


96  THIRD   YEAR  [Written 

PRACTICAL    PROBLEMS 

1.  A  huckster's  sales  for  the  week  were  as  follows : 
$  3.25,  S  7.15,  $  2.45,  $  6.45,  and  $  8.79.  What  was  the 
amount  of  bis  sales  ? 

2.  A  boy's  suit  that  was  marked  $  6.98  was  sold  for 
$  1.25  less.     What  was  the  selling  price  of  the  suit  ? 

3.  James  had  $  5.94  ;  he  spent  $  2.85.  How  much 
had  he  leit  ? 

4.  What  is  the  difference  in  the  price  of  two  hats 
marked  $  4.50  and  $  3.60  ? 

5.  The  following  amounts  were  deposited  in  the 
school  savings  bank:  $2.15,  $1.65,  $7.09,  $3.68,  and 
$9.15.     What  was  the  total  of  these  deposits? 

6.  Mrs.  Jones  paid  $2.75  for  a  turkey,  $.30  for 
cranberries,  $  .15  for  butter,  and  $  .48  for  coffee.  What 
was  the  whole  cost  ? 

7.  How  many  school  badges  4  in.  long  can  be  made 
from  2  vd.  of  ribbon  ? 

8.  A  clock  that  strikes  the  half  hours  strikes  how 
many  times  in  a  day  ? 

9.  How  many  square  inches  are  there  in  an  8-inch 
square  ? 

10.  There  are  639  oranges  in  9  baskets,  with  the  same 
number  in  each.     How  many  are  there  in  each  basket  ? 

11.  If  yoii  receive  $2.75,  $6.96,  and  $8.15  and  want 
to  change  it  into  five-dollar  bills,  how  many  should  you 
get  and  how  much  money  over? 


Oral  and  Written]      MULTIPLICATION  97 

COMPARISON 

1.  Compare  10  with  5;  thus,  10  is  two  times  5. 

2.  Compare  5  with  10;  thus,  5  is  |  of  10. 

Note. — We  might  also  compare  5  with  10  by  saying  10  is  5 
more  than  5;  but,  unless  otherwise  stated,  "compare"  in  this 
book  means  "find  the  quotient  of  the  first  number  divided  by  the 
second." 

3.  Compare  30  with  10;  20  with  5;  24  with  6. 

4.  Compare  5  with  15;  8  with  24;  12  with  48. 

5.  Compare  40  with  10;  with  8;  with  5;  with  4. 

6.  Compare  25  with  5;  5  with  25. 

7.  When  2  pencils  cost  10^,  how  much  will  8  cost? 

8.  When  6  hats  cost  $12,  how  much  will  12  cost? 

9.  When  4  knives  cost  $6,  how  much  will  8  cost? 

10.  At  6  pens  for  10^,  how  much  will  18  cost? 

11.  When  6  horses  cost  $900,  how  much  will  24  cost? 

24  horses  are  4  times  6  horses.  Hence,  they  will  cost  4  x  $900, 
or  $3600. 

12.  When  5  cows  cost  $160,  how  much  will  30  cost? 

13.  When  3  barrels  of  apples  cost  $7.50,  how  much 
will  12  cost? 

14.  If  5  tons  of  hard  coal  cost  $32.50,  how  much  will 

30  tons  cost? 

15.  At  $45  for  60  bu.  of  wheat,  how  much  will  12 
bu.  cost? 

16.  If  12  men  earn  $51  in  one  day,  how  much  will 
60  men  earn  in  one  day  at  the  same  rate? 


98 


THIRD   YEAR 


[Oral 


MEASURES  OF  TIME 

1.  Name  the  letters  on  the  face 
of  the  clock.     Tell  the  time. 

2.  Observe  the  small  spaces  on 
the  outer  edge  of  the  face.  These 
are  called  minute  spaces. 

3.  Over  how  many  of  these  spaces 
does  the  long  or  minute  hand  move 

in  passing  around  the  face  from  XII  to  XII  again  ? 

4.  How  long  is  the  minute  hand  in  passing  from 
XII  to  I?   from  V  to  VI?   from  X  to  XI  ? 

5.  There  are  the  same  number  of  minute  spaces 
hetween  any  two  hours. 

6.  While  the  minute  hand  passes  from  XII  to  XII 
again,  how  far  does  the  short  or  hour  hand  move  ? 

7.  How  many  minutes  are  there  in  an  hour?  in 
2  hr.  ?   in  4  hr.  ?   in  i  hr.  ? 

8.  When  the  hour  hand  is  at  XII,  what  is  the  time 
if  the  minute  hand  points  to  V  ?   to  III  ?   to  I  ? 

9.  Count  the  hours  on  the  clock  face  from  9  o'clock, 
the  opening  of  school,  until  9  o'clock,  the  next  morn- 
ing. How  many  are  there  ?  These  24  hours  include 
both  day  time  and  night  time. 


60  minutes  =  1  hour ;  written,  60  min.  =  1  hr. 
24  hours  =  1  day;  written,  24  hr.  =  1  da. 


Oral] 


MEASURES   OF  TIME 


99 


The  day  always  begins  at  XII,  midnight.  The  time 
from  midnight  to  noon  is  called  forenoon.  The  time 
from  XII,  noon,  to  midnight  is  called  afternoon. 

We  write  A.M.  for  forenoon  and  P.M.  for  after- 
noon. 8 :  20  A.M.  is  read  20  minutes  past  eight  in  the 
morning. 

10.  Read  6:10  a.m.;  4:25  a.m.;  6:30  p.m.;  6:45 
P.M.;    10:00  A.M.;  5:05  P.M. 

11.  How  many  hours  is  it  from  9  a.m.  to  5  p.m.? 
from  10  P.M.  to  6  a.m.  ? 

12.  How  many  days  is  it  from  9  o'clock  Monday 
morning  to  9  o'clock  the  next  Monday  morning? 


7  days  =  1  week ;  written,  7  da.  =  1  wk. 


13.  On  what  day  did  Feb.  1, 
1907,  fall  ?  Make  a  calendar  for 
February,  1907,  similar  to  the  one 
for  January. 

14.  Name  the  months  of  the 
year,  beginning  with  January. 


•907jANUARy'907| 

SUN 

MON 

TUE 

WED 

THU 

FRI 

SAT 

.. 

.. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

" 

•• 

12  months  =  1  year ;  written,  12  mo.  =  1  yr. 


15.  How  many  months  are  there  in  8  years  ? 

16.  How  many  days  are  there  in  6  weeks  ? 

17.  How  many  hours  are  there  in  9  days  ? 

18.  How  many  minutes  are  there  in  4  hours  ? 


100 


THIRD  YEAR  [Oral  and  Written 


MEASURES   OF   SURFACE 

1.  Draw  a  square    1    inch  long  and    1   inch   wide. 
What  shall  we  call  it  ? 

2.  Draw  on  the  blackboard  a  square  1  foot  long  and 
1  foot  wide.     Call  it  a  square  foot. 

3.  Draw  on    the  blackboard  a  square  1   yard   long 
and  1  yard  wide.     Call  it  a  square  yard. 

4.  Separate  by  points,  each 
side  of  the  square  yard  into  3 
equal  parts.  Connect  these 
points  by  straight  lines.  What 
is  the  size  of  each  square  ?  How 
many  square  feet  are  there  in 
a  square  yard  ? 

5.  This  picture  shows  a 
square  yard,  smaller  than  it  really  is.  How  many 
square  feet  does  it  show  ? 


On 


e    squ  are 


yard 


9  square  feet=l  square  yard;  written,  9  sq.  ft.  =  l  sq.  yd. 


6in 


6.  This  picture .  shows  an 
oblong  6  inches  by  4  inches. 
Divide  it  into  square  inches. 
How  many  square  inches  are 
there  in  one  row  ?  in  2  rows  ? 
in  3  rows  ?  in  4  rows  ? 

In  1  row  there  are  6  sq.  in. 


In  4  rows  there  are  4x6  sq.  in.  =  24  sq.  in. 


Written]  SURFACES  101 

SURFACES 
Draw  figures  and  find  the  number  of  square  inches  in  : 

1.  An  oblong  1  in.  wide  and  4  in.  long. 

2.  An  oblong  2  in.  wide  and  6  in.  long. 

3.  An  envelope  2  in.  wide  and  6  in.  long. 

4.  A  blotter  3  in.  v^ide  and  6  in.  long. 

5.  A  page  4  in.  wide  and  6  in.  long.  ■  -  '>;' 

6.  A  square  3  in.  on  a  side.  ,    v    _     : ,.  .     .''  v 

7.  A  square  4  in.  on  a  side. 

8.  The  top  of  a  box  5  in.  on  a  side. 

9.  A  picture  4  in.  by  6  in. 

With  one  inch  representing  a  foot,  draw  figures  and 
find  the  number  of  square  feet  in: 

10.  A  rug  3  ft.  wide  and  8  ft.  long. 

11.  A  hallway  4  ft.  wide  and  10  ft.  long. 

12.  A  table  cover  7  ft.  by  4  ft. 

13.  A  window  glass  4  ft.  by  9  ft. 

14.  The  glass  for  a  picture  2  ft.  by  3  ft. 

With  one  inch  representing  a  yard,  draw  figures  and 
find  the  number  of  square  yards  in : 

15.  A  room  4  yards  by  6  yards. 

16.  A  porch  floor  2  yards  wide  and  8  yards  long. 

17.  A  hallway  3  yards  wide  and  12  yards  long. 

18.  A  rug  3  yards  wide  and  5  yards  long. 

19.  A  porch  rug  2  yards  wide  and  4  yards  long. 

20.  A  wall  3  yards  in  height  and  6  yards  long. 

21.  A  blackboard  1  yard  in  height  and  8  yards  long. 


102  THIRD  YEAR  [Written 

PRACTICAL  PROBLEMS 

Market  Report 

Apples.     Best,  $2.25;  Eggs.    18<*perdoz. 

Fair  grades,  $  1.50  per  bbl.  Butter.     Creamery,  28  f  per  lb. ; 
Peaches.     Good,  $2.25;  Dairy,  25  ^  per  lb. 

Fancy,  $2.50  per  bu.  Cheese.     Full  cream,  12|^  per  lb. 
Pears.     Best,  $1.50  per  bu.  American,  15^  per  lb. 

Grapes.     .Niagara,   25^    per    10-lb.  Potatoes.    50^'perbu. 

.  bjiskst.         ^  Sweet  potatoes.    Virginia,  80^ ; 

Concords,  28  ^  per  10-lb.  basket.  Jersey,  $  1.25  per  bu. 

Frdni  this  market  report  find  the  cost  of  the  following : 

1.  8  bu.  of  fancy  peaches. 

2.  4^  lb.  of  butter,  creamery. 

3.  5|  bu.  of  potatoes. 

4.  8  10-lb.  baskets  of  Concord  grapes. 

5.  7  bbl.  of  apples,  best  quality. 

6.  9  cases  of  eggs,  30  dozen  each. 

7.  8  10-lb.  baskets  of  Niagara  grapes. 

8.  8|-  bu.  of  sweet  potatoes,  Virginia. 

9.  7  bu.  of  peaches,  good. 

10.  9  full  cream  cheese,  15  lb.  each. 

11.  7  10-lb.  baskets  of  Concord  grapes. 

12.  9J  bu.  of  pears,  best  quality. 

13.  8  bbl.  of  apples,  fair  grades. 

14.  7  lb.  of  creamery  butter  and  32  lb.  of  dairy  butter. 

15.  8  bu.  of  fancy  peaches,  and  42  bu.,  good  quality. 

16.  8    10-lb.    baskets    of    Concord    grapes,    and    6 
10-lb.  baskets  of  Niagara  grapes.     . 


Written]  REVIEW  OF  THIRD  YEAR  103 

REVIEW   OF    THIRD   YEAR 

1.  There  are  8  pints  in  one  gallon.  How  many 
pints  are  there  in  36  gallons  ? 

2.  A  train  runs  26  miles  in  1  hour.  How  far  can 
it  run  in  9  hours  ? 

3.  How  much  will  8 J  yards  of  cloth  cost  at  32  cents 
per  yard  ? 

4.  At  the  rate  of  9  pages  an  hour,  how  long  will 
it  take  to  finish  a  story  of  27  pages  ? 

5.  Nine  girls  spent  $4.95  at  a  picnic.  What  was 
the  average  amount  spent  by  each  ? 

6.  At  6  cents  a  pound,  how  many  pounds  of  sugar 
can  be  bought  for  138  cents  ? 

7.  There  are  168  cabbage  plants  in  8  rows.  How 
many  are  there  in  each  row  ? 

8.  James  saves  $  7  a  week  from  his  wages.  How 
long  will  it  take  him  to  pay  for  a  lot  valued  at 
$238? 

9.  A  drover  paid  $2040  for  sheep  at  $6  a  head. 
How  many  did  he  buy  ? 

10.  Eight  lamps  cost  $17.28.     Find  the  cost  of  one. 

11.  How  many  bushels  equal  396  pecks  ? 

12.  How  many  gallons  equal  792  pints  ? 

13.  How  many   tons  of  coal  at   $6  a  ton  can    be 
bought  for  $786? 

14.  How  much  milk  at  8  cents  a  quart  can  be  bought 
for  $2.56?     ($2.56  =  256^.) 


104  THIRD   YEAR  [Written 

15.  I  paid  $12.54  for  berries  at  6  cents  a  box.  How 
many  boxes  did  I  buy  ? 

16.  A  man  divided  $875  among  his  7  cbildren. 
How  much  did  each  child  receive  ? 

17.  How  many  weeks  are  equal  to  287  days  ? 

18.  If  9  hours'  work  is  counted  as  a  day's  work,  for 
how  many  days  should  a  man  be  paid  who  has  worked 
342  hours  ? 

19.  6  melons  cost  78  cents.  How  much  is  that 
apiece  ? 

20.  How  many  yards  equal  54  feet  ? 

21.  At  48  cents  a  gallon,  what  is  the  cost  of  a  pint 
of  molasses  ? 

22.  If  6  barrels  of  apples  cost  $13.50,  what  is  the 
cost  of  1  barrel  ? 

Find  the  cost  of : 

23.  8  hats  @  $3.  29.  7  pr.  shoes  @  $41 

24.  7  beds  @  $9.  ^    30.  12  melons  @  8^. 

25.  7  qt.  milk  @  8^.  3i.  6  bbl.  flour  @  $4i. 

26.  8  books  @  $2.  32.  71  lb.  sugar  @  8^. 

27.  4  gal.  oil  @  25^.  33.  8  yd.  of  cloth  @  50^. 

28.  6  chairs®  $3^.  34.  8  spools  tliread  @  10^. 

35.  Eight  men  paid  $2.50  each  to  the  Fresh  Air 
Fund.     How  much  was  given  by  all  ? 

36.  Mr.  Brown  paid  $400  for  8  acres  of  land.  How 
much  were  24  acres  worth  ? 


Written]  REVIEW  OF  THIRD  YEAR  105 

37.  Seven  o'clock  a.m.  is  how  many  hours  after  mid- 
night ? 

38.  144  square  inches  make  one  square  foot.  How 
many  square  inches  equal  8  square  feet  ? 

39.  At  $  7.50  each,  how  much  will  7  suits  of  clothing 
cost  ? 

40.  How  much  will  8|-  pounds  of  pork  cost  at  12^  a 
pound? 

41.  At  $  4.75  each,  how  much  will  8  hats  cost  ? 

42.  Mrs.  White  paid  $  2.25  a  yard  for  velvet.  How 
much  would  she  pay  for  7  yards  at  the  same  rate  ? 

43.  Joseph  Black  employs  8  clerks  at  a  salary  of 
$  15.50  a  week  each.  How  much  must  he  pay  his 
clerks  at  the  eud  of  the  week  ? 

44.  At  3  palings  to  the  foot,  how  many  palings  are 
required  for  a  fence  12  yards  and  2  feet  in   length  ? 

45.  How  much  will  an  8J  pound  roast  of  veal  cost  at 
16^  a  pound? 

46.  8  gallons  of  ice  cream  were  sold  at  15^  a  pint. 
How  much  was  received  for  it  ? 

47.  At  25^  a  peck,  for  how  much  will  2  bu.  of  toma- 
toes retail  ? 

48.  A  man  sold  a  horse  for  $230  and  lost  $56. 
How  much  did  the  horse  cost  him  ? 

49.  Mr.  Frank  rented  a  house  at  $  360  a  year.  How 
much  rent  will  he  pay  in  7|  years? 


106  THIED  YEAR  [Written 

50.  A  man  hires  a  horse  for  35^  an  hour.  How  much 
must  he  pay  if  he  uses  the  horse  from  10  a.m.  until 
5  p.m.? 

51.  A  man  bought  a  lot  for  $  1275.  He  built  a  store- 
room on  it  for  $  2450.  He  sold  the  property  for  $  5000. 
Find  his  gain. 

52.  What  is  the  weight  of  6  sacks  of  wheat,  each 
weighing  168  pounds? 

53.  How  much  will  8|  tons  of  coal  cost  at  $  4.50  a 
ton? 

54.  9  tons  of  coal  for  a  school  cost  $  38.25.  How 
much  was  that  a  ton  ? 

55.  A  school  has  2  floors,  with  4  rooms  on  each  floor. 
How  many  pupils  are  there  in  the  school,  if  there  are 
36  pupils  in  each  room  ? 

56.  A  teacher  in  this  school  earns  $  65  per  month, 
and  spends  $  35.  How  much  does  he  save  in  9 
months  ? 

57.  Find  the  cost  of  8 J  yards  of  dress  goods  at  48 
cents  per  yard. 

58.  A  pair  of  shoes  costs  $2|.  How  much  will  7 
pairs  cost? 

59.  If  I  pay  96  cents  for  3  yards  of  ribbon,  how  much 
should  I  pay  for  1  yard  ?  for  1^  yards  ? 

60.  The  distance  from  New  York  to  Pittsburg  is  444 
miles.  What  is  the  fare  for  a  round  trip,  at  2^  per 
mile  ? 


PART   III  — FOURTH   YEAR 

READING   AND   WRITING   NUMBERS 

Review  pages  29,  30,  and  72. 

For  convenience  in  reading  large  numbers,  the  figures 
are  generally  separated  by  commas  into  groups  of  three 
figures  each,  called  periods. 

The  first  period,  counting  from  the  right,  is  units ; 
the  second,  thousands ;  the  third,  millions. 

The  following  table  shows  the  arrangement  of  th^se 
periods,  and  the  three  orders  of  figures  in  each  period : 


Millions'  Period 

Thousands'  P 

ERIOD 

Units' 

Period 

is 

§    3 

n 

CO 

5 

09 

i 

on 

1 

-o  .2 
MS 

Teu- 
millio 

Millie 

II 

il 

2 

0     4, 

6 

4 

L 

3 

7    6 

The  number  in  the  table  is  read,  "  204  million,  641 


thousand,  376. 

J) 

Copy,  point 
a 
1.      2000 

off,  and  read : 
b 
20135 

c 
81125 

d 
125125 

2.    20000 

20648 

48760 

625840 

3.    21000 

56506 

40084 

1760894 

4.    36000 

94600 

61006 

8300404 

107 


108  FOURTH   YEAR        [Oral  and  Written 

READING  AND  WRITING  NUMBERS 

Express  in  figures : 

1.  Forty-two  thousand. 

2.  Sixty-six  thousand  four. 

3.  Seventy-five  thousand  fifty. 

4.  Thirty-nine  thousand  one  hundred  twenty-two. 

5.  Two  hundred  ten  thousand  three  hundred  fifty. 

6.  Five  hundred  sixty-five  thousand  one  hundred. 

7.  One  million  one  hundred  twenty-five  thousand. 

8.  Three  million  six  hundred  thousand  thirty-five. 

9.  Twenty-five  million  nine  thousand  twenty-six. 

10.  Eighty  million  twenty-six  thousand  sixty-four. 

11.  Nine  hundred  thousand  nine. 

12.  Forty-six  million  four  thousand  sixteen. 

13.  One  hundred  ten  million  five  hundred. 

14.  Three  hundred  thirty-six  million  one  hundred  four. 

15.  Five  hundred  seven  million  five  thousand  six. 

16.  Seventeen  million  three  thousand  seventy-five. 

17.  One  million  two  thousand  seven  hundred  four. 

18.  1  million,  104  thousand,  185. 

19.  21  million,  110  thousand,  109. 

20.  604  million,  622  thousand,  468. 

21.  101  million,  10  thousand,  10. 


Oral  and  Written]     ADDITI0:N"  AND   SUBTKACTION     109 

ADDITION   AND   SUBTRACTION 

Review  pages  32  to  43,  54,  55,  63,  64,  65,  73,  91,  and  92. 

1.  Count  by  4's  from  2  to  100 ;  from  3  to  99. 

2.  Count  by  G's  from  o  to  99  ;  from  5  to  101. 

3.  Count  by  8's  from  3  to  99  ;  from  4  to  100. 
Add  the  following,  allowing  five  minutes  for  each : 

abed 

4.  $32.45   -f    $50.75   +    $32.11   +    $32165  = 
61.79    +        1.24   +        2.84   +         94.76  = 

8.15   +        6.19    +      16.31    +  8.92  = 

23.42   +      83.72   +        5.49    +      143.74  = 
94.76   +        9.85   +      26.32    +        25.81  = 


$  +$  +$  +$             = 

5.    $35.18  +    $85.24  +    $21.89  +    $  86.42  = 

92.76  +        8.93  +       39.65  +        93.84  = 

9.84  +      16.82  +       84.21  +          2.69  = 

26.37  +      73.25  +       16.93  +        39.87  = 

81.74  +        4.68  +       12.85  +        71.44  = 


$  +$•  +$  +$  =$ 

Subtract,  allowing  one  half  minute  for  each : 

a  b  c  d 

6.  $275.43    $536.75    $408.37    $674.26 
167.35     308.28     286.58     210.75 


7.  $682.72    $826.45    $527.05    $763.72 
79.80      60.76      89.98     140.80 


110  FOURTH  YEAR  [Written 

PRACTICAL   PROBLEMS 

1.  A  man  paid  $2.50  for  a  hat  and  $15.50  for  a 
suit.     How  much  did  he  pay  for  both  ? 

$  2.50,  cost  of  hat. 

15.50,  cost  of  suit. 

$  18.00,  cost  of  both. 

2.  A  merchant  sold  425  bu.  of  potatoes,  232  bu.  of 
apples,  aiid  189  bu.  of  onions.  Find  the  total  number 
of  bushels  sold. 

3.  A  lady  paid  $25  for  a  carpet,  $71  for  a  rug,  and 
$  7  for  curtains.     What  was  the  amount  of  her  bill  ? 

4.  How  many  days  are  there  in  the  last  six  months 
of  the  year  ? 

5.  A  man  left  his  estate  to  his  wife,  son,  and  daughter. 
His  wife  received  $9845,  his  son  $3650,  and  his  daugh- 
ter $3500.     What  was  the  value  of  the  whole  estate? 

6.  I  sold  my  house  for  $5675,  thereby  losing  $897. 
How  much  did  the  house  cost  ? 

7.  A  lawn  is  30  ft.  long  and  24  ft.  wide.  How  many 
feet  is  it  around  the  lawn  ? 

8.  New  York  is  327  miles  east  of  Altoona  by  rail- 
road and  Pittsburg  is  117  miles  west.  How  far  is  it 
from  New  York  to  Pittsburg  ? 

9.  The  pupils  of  a  school  deposited  money  in  a  sav- 
ings bank  as  follows :  January,  $  16.45 ;  February, 
$  14.60  ;  March,  $  18.35  ;  and  April,  $  17.51.  Find  the 
total  deposits. 


Written]  SUBTEACTIOK  111 

PRACTICAL   PROBLEMS 

1.  A  ranchman  bought  468  cows  and  sold  239  of 
them.    How  many  had  he  left? 

468,  number  of  cows  bought. 

239,  number  of  cows  sold. 

229,  number  of  cows  remaining. 

2.  Mr.  Jones  was  born  in  1851.  How  many  years 
old  is  he  if  now  living  ? 

3.  A  man's  property  sells  for  $47892.  He  ow^es 
$36987.  How  much  has  he  left  after  paying  all  his- 
debts  ? 

4.  In  a  certain  election  A  received  38714  votes  and 
B  29867  votes.     How  much  did  A's  vote  exceed  B's? 

5.  I  sold  a  farm  for  $5628,  which  w^as  at  a  gain  of 
$1394.     What  was  the  cost  of  the  farm  ? 

6.  A  merchant  bought  26520  bu.  of  grain  and  sold 
18296  bu.     How  many  bushels  had  he  left? 

7.  The  population  of  a  town  is  8596.  Ten  years 
ago  it  was  2397.     What  was  the  increase  in  ten  years  ?* 

8.  A  man's  salary  is  $2525  a  year.  His  expenses 
are  $1786.     How  much  can  he  save  in  a  year? 

9.  A  barrel  of  flour  weighs  200  lb.  The  barrel  itself 
weighs  4  lb.  How  many  pounds  of  flour  are  there  in  a 
barrel  ? 

10.  At  an  election  the  whole  number  of  ballots  cast 
was  11342.  Of  this  number  A  received  8673.  How^ 
many  votes  were  cast  for  his  opponent  ? 


112 


FOURTH    YEAR 


[Oral 


MULTIPLYING  BY   lo 

Review  pages  56,  59,  66,  79,  80,  85,  and  86. 

1.  Count  by  lO's  to  100.     Build  the  table  of  lO's. 

2.  How  many  are  9  X  10  ?    90  +  ?=  100. 

3.  Place  a  naught  to  the  right  of  4.  What  number 
have  you  ?  40  is  how  many  times  four  ?  Place  a  naught 
to  the  right  of  6;  3;  7;  9;  11;  12.  See  whether 
each  product  has  become  ten  times  the  minuend. 

Annexing  a  naught  to  the  right  of  a  number  multiplies 
it  hy  10. 

4.  Annex  0  to  each  number.     Notice  the  effect: 
4        20         36         75        42         87         275 

93    87   692   387   509   938    765 

5.  Memorize  the  table. 

6.  Compare : 

10  X    5  with    5  X  10 
8  X  10  with  10  X    8 

11  X  10  with  10  X  11 
40  and  80         100  and  10 

120  and  12         110  and  11 

Find  the  cost  of : 

7.  10  newspapers  @  5^.  ii.  91  lb.  lard  @  10^. 

8.  8  ladies' hats  @  $  5.  12.  12^  doz.  buttons  @  10^. 

9.  10  oranges  @  2  for  5^.  13.  10  qt.  milk  @  8^. 

10.    101  yd.  muslin  @  12  ^.  i4.    101  bu.  tomatoes  @  80^. 


Table 

of   lO'S 

1x10=10 

7x10=    70 

2x10  =  20 

8x10=    80 

3x10  =  30 

9x10=    90 

4x10  =  40 

10x10=100 

5  X  10  =  50 

11x10=110 

6x10=60 

12x10  =  120 

ral] 


MULTIPLICATIOK 


113 


I 

WF  MULTIPLYING   BY   ii 

1.    Count  by  ll's  to  33;  to  66;  to    99.     Build  the 
table  of  ll's. 

2.9x11=?     99  +  11=?     How  many  irs  =  110? 

3.  10  X  11  =?  10  times  11,  plus  11  =  ?     How  many 
are  11x11? 

4.  To  find  12  x  11  how  many  must 


be  added  to  11  x  11  ? 

12x11=  ? 

5.    Give  at  sight : 

10x11          12x11 

5x11 

3x11           4x11 

8x11 

6x11          11  X    9 

llx    7 

Table  of 

II'S 

1x11 

=  11 

7 

xll  = 

77 

2x11 

=  22 

8 

xll  = 

88 

3x11 

=  33 

9 

xll  = 

99 

4x11 

=  44 

10 

xll  = 

110 

5x11 

=  55 

11 

xll  = 

121 

6x11 

=  66 

12 

xll  = 

132 

6.  Memorize  the  table. 

7.  Compare  : 

11  X    7  with    7  X  11 
9  X 11  with  11x9 

11  X    4  with    4  X  11 

12  X  11  with  11  X  12 
6x11  with  11  X    6 


8.  Find  the  products  : 

11x60  11x80         11x40       11x100 

11x90  11x50         11x20       llx    80 

11x13  11x30        11x70       llx    15 

Find: 

9.  j\  of  132  ;  of  88 ;  of  121 ;  of  110. 


11  X  30 
11  X  25 
11x18 


114 


FOURTH  YEAR        [Oral  and  Written 


MULTIPLYING   BY   12 

1.    Count  by  12's  to  36  ;  to  72  ;  to  144.     How  many 
are  12  times  12  ?     Build  the  table  of  12's. 

Table  of  12's  2.    Memorize  the  table. 


1x12  =  12 

7x12=   84 

2x12  =  24 

8x12=    96 

13x12  =  36 

9x12  =  108 

4  X  12  =  48 

10x12  =  120 

t5x  12  =  60 

11x12  =  132 

6x12  =  72 

12x12  =  144 

3.   Multiply  bj 

-  12;  by  11: 

465 

236         789 

546 

783        928 

784 

937         693 

785 

514        938 

978 

694        296 

1  dozen  =12        1  gross  =  144 


4.    "What  two  numbers  make  the  following  products  ? 
25   27      28     30     32     35     36     40     42     45     48 
49   56     60     63     64     66     72     80     84     88     96 

MULTIPLICATION  BY  A  MIXED  NUMBER 


1.    Multiply  34  by  4^-.    4^  times  34  means  that  ^  of 
34  34  is  to  be  added  to  4  x  34. 

41 

17  =  i  of  34  Find  the  products: 

136  =  4  times  34  2.    8^  x  48  4.    8}  x  120 

5.    6ixl80 


153  =  41  times  34 


2.  81x48 

3.  91x72 


€.   71x84 


7.   51x242 


8.   121x224 


rral]  DIVISIOiT  115 

DIVIDING    BY   10 

1.  Begin  with  0  and  count  by  lO's  to  100.  Begin- 
ning with  1  count  by  lO's  to  101. 

2.  50  is  how  many  times  5  ?  How  does  60  compare 
with  6  ?  Remove  zero  from  80.  What  is  the  result  ? 
8  is  what  part  of  80  ? 

3.  Remove  naught  from  30;  from  90;  from  70.  How 
does  the  result  in  each  case  compare  with  the  number? 

4.  3  is  what  part  of  30  ?  4  is  what  part  of  40? 
J5of40  =  ? 

Removing  a  naught  from  the  right  of  ariy  number 
divides  it  hi/  10. 

5.  Divide  by  10 :    Complete  in  two  minutes. 

40  30  90  80  60  100  120 

320  560  980  750  360  470  920 

1450  1680  2450  1930  2210  9990  7400 

6320  4040  3100  2010  8500  7280  6900 

6.  How  many  10-cent  balls  can  be  bought  for  $1.00? 
for  $2.00?  for  $5.00? 

7.  At  10  cents  a  quart,  how  many  quarts  of  milk  can 
be  bought  with  $2.80  ? 

8.  How  long  will  it  take  a  motor  car  going  10  miles 
an  hour  to  travel  140  miles  ? 

9.  If  I  pay  50^  for  a  telegram  pf  10  words,  how 
much  do  I  pay  for  each  word  ? 


116  FOURTH  YEAR        [Oral  and  Written 

DIVIDING   BY    II    AND    i2 

1.  Subtract  by  ll's  from  132  to  0. 

2.  State  quotients  at  3igbt : 

33^11  66^11  88^11  132-^ll 

44^11  77-^11  99H-11  121^11 

3.  Find  ^3^  of :   88  ;  99  ;  22  ;  78  ;  33  ;  48  ;  44  ;  55 ; 
69;   11;  66;  81;  77;  92;  88;  99;  110;  121;  83. 

Divide  by  11 :     Test  answers. 

4.  2738            7.   6954            lo.  8923  13.  69753 

5.  8294            8.   3986             11.  2158  i4.  73065 
€.   2036            9.   3007            12.  8057  15.  90074 

16.  Subtract  by  12's  from  144  to  0. 

17.  State  quotients  at  sight : 


36-^12 

60^12 

84^-12 

132^12 

24^12 

96^12 

108^12 

144^12 

18.    Find   ^3^    of:    96;  84;  72;   36;  108;  24;  120; 
132;  60;  48;  144. 

Divide  by  12  :  Test  answers. 

19.  3678     24.  7817    29.  42192    34.  91875 

20.  4135     25.  2936    so.  69378  35.  24726 

21.  6973     26.  9238    31.  73945  36.  68359 

22.  7128     27.  4697    32.  82659  37.  81763 

23.  4693     28.  9384    33.  37296  38.  92364 


Oral] 


MULTIPLICATION   AND  DIVISION 


117 


REVIEW 


Find  the  cost  of : 

1.  9  rings  @  $3 

2.  12  cows  @  $35 

3.  10  hats  @  $3.65 

4.  10  rugs®  $1.50 

5.  3  wagons  @  $85 

6.  9  plates®  $1.75 

7.  10  knives®  $.75 
Find  the  cost  of  1,  when : 

15.  12  lamps  cost  $51 

16.  4  cases  cost  $32.48 

17.  10  sleds  cost  $19.50 

18.  10  sheep  cost  $45.00 

19.  11  desks  cost  $35.75 

20.  8  trunks  cost  $57.60 

21.  10  clocks  cost  $48.50 

22.  5  hats  cost  $15 

23.  12  hats  cost  $27 

24.  8  lb.  rice  cost  96^ 

25.  3  clocks  cost  $9.75 

26.  9  books  cost  $11.25 

27.  5  chairs  cost  $15.45 

28.  9  lb.  nuts  cost  $2.25 

29.  8  bu.  coal  cost  $1.20 


8.  10  vases  @  $2.39 

9.  10  horses  ®  $95 

10.  11  books  ®  $2.25 

11.  11  sheep  ®  $4.75 

12.  10  chairs  ®  $5.25 

13.  6  chickens  ®  75^ 

14.  12  pictures®  $4.50 

30.  10  satchels  cost  $35.50 

31.  12  yd.  lace  cost  48  ^ 

32.  11  lb.  steak  cost  $1.98 

33.  6  gal.  vinegar  cost  72^ 

34.  12  bu.  potatoes  cost  $9 

35 .  1 2 .  pk .  t  omatoes  cost  $  3 

36.  10  toy  engines  cost  $35 

37.  5  lb.  steak  cost  $1.10 

38.  8  qt.  cream  cost  $1.60 

39.  4  bu.  cherries  cost  $15 

40.  10  yd.  silk  cost  $17.50 

10  pt.  cream  cost  $1.10 

11  lb.  butter  cost  $2.20 

43.  3  pairs  shoes  cost  $9.75 

44.  12  collars  cost  $2.40  . 


41. 
42. 


118  FOURTH  YEAR  [Written 

REVIEW 

1.  A  train  runs  378  miles  in  7  hours.  How 
many  miles  is  that  in  1  hoar? 

2.  A  ticket  agent  has  $  5.85  in  his  drawer.  After 
selling  2  tickets  at  90^  each,  8  tickets  at  70^  each,  and 
1  mileage  book  for  $  20,  how  much  money  should  his 
drawer  contain  ? 

3.  While  the  hour  hand  is  going  8  times  around 
the  dial  how  often  does  the  minute  hand  go  around  ? 

4.  The  treasury  of  a  school  district  contains  $  2642. 
After  paying  the  salaries  of  six  teachers  for  8  months 
at  $45  per  month,  how  much  remains? 

5.  A  farmer  sold  4  jars  of  butter  containing  re- 
spectively, 24  pounds,  27  pounds,  26  pounds,  and  33 
pounds.     How  many  pounds  did  he  sell  ? 

6.  A  newsboy  earns  30  cents  a  day.  How  much 
will  he  earn  in  4  weeks  of  6  days  each  ? 

7.  What  is  left  from  a  $  10  bill  after  paying  for  lOJ 
lb.  of  tea  at  60  cents  a  pound  ? 

8.  The  expenses  for  a  family  for  a  year  are  as  follows  : 
food,  $485;  fuel  and  light,  $86  ;  car  fare,  $35;  cloth- 
ing, $  285  ;  church,  $  68  ;  books  and  papers,  $  25  ;  ser- 
vant, $165;  other  expenses,  $278.  Find  the  entire 
expenses. 

9.  In  a  school  of  897  pupils,  there  are  487  girls. 
How  many  boys  are  there? 


Written]  EEVIEW  119 

DRILL  WORK 

Write  and  add  : 

a  b  c 

1.  $2785.00  $5870.00  $475.00 

597.55  29.60  6000.00 

3000.00  587.25  459.06 

987.46  45.03  250.00 

6750.00  6540.20  4278.64 

5340.02  8750.00  5782.98 

9876.54  2346.59  8796.32 

3201.89  4567.83  4123.56 

2.  $6004.50  $6550.00  $2987.35 

500.83 

6789.05 
200.06 
678.46 
4586.23 
2080.95 
2345.10 

3.  $475.00  $1286.40  $7665.00 

.  2050.50 

2002:02 
879.30 
698.09 

5000.10 
898.45 

4987.56 


$6004.50 

$6550.00 

887.95 

278.93 

504.06 

8.10 

2874.59 

200.02 

850.00 

7007.05 

2250.05 

520.84 

275.83 

4265.63 

7817.89 

6005.80 

$475.00 

$1286.40 

6000.20 

587.52 

579.80 

3873.20 

1000.50 

78.00 

457.39 

759.06 

100.10 

9300.00 

4555.05 

759.84 

7016.89 

5234.18 

120  FOURTH   YEAR  [Written 

DRILL   WORK 

Subtract  and  test  5  problems  in  1  minute. 

a  bed 

1.    $860.45  $874.61  $724.82  $870.62 

178.62  126.42  109.87  188.94 


2.  $684.26  $962.41  $921.08  $700.64 

397.84  802.96  120.09  188.96 

3.  $784.12  $908.07  $916.25  $864.30 

479.63  194.72  721.24  497.86 

4.  $876.42  $900.40  $921.11  $422.33 

91.76  87.80  888.66  188.88 


5.  $600.03  $744.44  $800.55  $111.21 

187.69  299.99  288.85  108.89 

6.  $700.77  $644.41  $854.32  $765.43 

188.99  387.64  123.45  112.34 

7.  $842.16  $964.21  $841.22  $742.24 

199.97  188.74  108.62  604.28 

8.  $914.79  $30500  $965.06  $821.00 

549.86  128.95  578  98  367.89 


Oral] 


MULTIPLICATION 


121 


MULTIPLICATION   TABLE 

Review  and  memorize : 


1x1=  1 

Ix    2=   2 

Ix    3=   3 

Ix    4=   4 

2x1=    2 

2x    2=   4 

2x    3=   6 

2x    4=   8 

3x1=   3 

3x    2=   6 

3x    3=   9 

3x    4  =  12 

4x1=   4 

4x    2=   8 

4x    3  =  12 

4x    4  =  16 

5x1=   5 

5x    2  =  10 

5x    3  =  15 

5x    4  =  20 

6x1=   6 

6x    2  =  12 

6x    3  =  18 

6x    4  =  24 

7x1=    7 

7x    2  =  14 

7x    3  =  21 

7x    4  =  28 

8x1=   8 

8x    2  =  16 

8x    3  =  24 

8x    4  =  32 

9x1=   9 

9x    2  =  18 

9x    3  =  27 

9x    4  =  36 

10  X  1  =  10 

10  x    2  =  20 

10  X    3  =  30 

10  X    4  =  40 

11x1  =  11 

11  X    2  =  22 

11  X    3  =  33 

11  X    4  =  44 

12  X  1  =  12 

12  x    2  =  24 

12  X    3  =  36 

12  X    4  =  48 

1X5=   5 

IX    6=   6 

Ix    7=   7 

Ix    8=   8 

2  X  5  =  10 

2x    6  =  12 

2x    7  =  14 

2x    8  =  16 

3x5  =  15 

3x    6  =  18 

3x    7  =  21 

3x    8  =  24 

4  X  5  =  20 

4x    6  =  24 

4x    7  =  28 

4x    8  =  32 

5  X  5  =  25 

5x    6  =  30 

5x    7  =  35 

5x    8  =  40 

6  X  5  =  30 

6x    6  =  36 

6x    7  =  42 

6x    8  =  48 

7  X  5  =  35 

7X    6  =  42 

7x    7  =  49 

7x    8  =  56 

8x5  =  40 

8x    6  =  48 

8x    7  =  56 

8x    8  =  64 

9x5  =  45 

9x    6  =  54 

9X    7  =  63 

9x    8  =  72 

10x5  =  50 

lOx    6  =  60 

10  X    7  =  70 

10  X    8  =  80 

11x5  =  55 

11  X    ^  =  66 

11  X    7  =  77 

11  X    8  =  88 

12  X  5  =  60 

12  X    6  =  72 

12  X    7  =  84 

12x    8  =  96 

1x9=     9 

1x10=   10 

1x11=  11 

1x12=   12 

2x9=   18 

2x10=   20 

2x11=   22 

2x12=   24 

3x9=    27 

3x10=   30 

3x11=   33 

3x12=   36 

4x9=   36 

4x10=   40 

4x11=   44 

4x12=   48 

5x9=    45 

5x10=    50 

5x11=   55 

5  X  12  =   60 

6x9=   54 

6  x  10  =   60 

6x11=    66 

6x12=   72 

7x9=    63 

7x10=   70 

7x11=   77 

7x12=   84 

8x9=    72 

8x10=   80 

8x11=   88 

8x12=   96 

9x9=   81 

9x10=   90 

9x11=   99 

9x12  =  108 

10x9=   90 

10x10  =  100 

10x11  =  110 

10x12  =  120 

11x9=   99 

11x10  =  110 

11x11=121 

11x12  =  132 

12x9  =  108 

12x10  =  120 

12x11  =  132 

12  x  12  =  144 

122  FOURTH  YEAR  [Oral 

MULTIPLIERS   ENDING   IN   NAUGHT 

1.  Annex  a  naught  to  the  right  of  3;  then  multiply 
3  by  10.     Is  there  any  difference  in  the  result  ? 

Annexing  a  naught  to  the  right  of  a  number  multiplies 
it  by  10. 

2.  Multiply  by  10:  40;  20;  60;  800;  300;  700;  900. 

3.  Multiply  3  by  100 ;  8  by  100 ;  9  by  100 ;  20  by  100. 
How  many  times  greater  has  each  of  the  numbers 
become?      How  many  naughts  were  added  to  each? 

Annexing  two  naughts  to  the  right  of  a  number  multi- 
plies  it  bylQO, 

4.  Find: 

100x4  100x15  100x50  100x75 

100x7  100x95  100x85  100x12 

100x5  100x37  100x91  100x36 

5.  What  is  the  difference  between  1000  x  3  and  3  x 
1000?   between  1000x6  and  6x1000?      How  many 
naughts  were  annexed  to  3  ?  to  6  ?     How  many  times 
greater  has  each  become? 

Annexing  three  naughts  to  the  right  of  a  number  multi- 
plies it  by  1000. 

6.  From  what  you  have  learned  make  a  rule  for 
multiplying  any  number  by  10  ;  100;  1000;  10000. 

7.  Multiply: 

8  by  1000;  7  by  1000;  9  by  1000;  4  by  1000;  13  by 
1000;  12  by  10000;  14  by  1000;  19  by  1000;  25  by 
100;  36  by  10;  95  by  100;  72  by  10;  72  by  10000. 


Oral  and  Written]      MULTIPLICATION  123 

1.  How  many  cents  are  there  in  100  dimes? 

2.  How  many  cents  are  there  in  $6? 

Find  the  weight  of: 

3.  1000  two-pound  packages  of  rolled  oats. 

4.  1000  five-pound  boxes  of  starch. 

5.  25  one  hundred-pound  kegs  of  nails. 

6.  100  lambs  at  an  average  of  45  lb.  each. 

7.  Find  the  cost  of  1000  one-cent  postal  cards  and 
100  two-cent  stamps. 

a  Multiply  63  by  2000. 

Write  the  2  of  the  multiplier  under  the  figure 
63  in  ones'  place  of  the  multiplicand.     2  x  63  is 

2000     126.     Annex  three  naughts  to  the  right  of  126, 
126000     making  1 26000.     1000  x  63  =  63000 ;  2000  x 
63  =  126000. 

Multiply,  and  read  the  product: 

9.   71  10.   85  11.  245  12.   715 

200  3000  4000  700 

13.  347  by  20  is.  293  by  500  23.  481  by  2000 

14.  409  by  30  19.  786  by  700  24.  894  by  4000 

15.  715  by  60  20.  184  by  400  25.  906  by  7000 

16.  329  by  80  21.  796  by  600  26.  728  by  9000 

17.  475  by  90  22.  832  by  200  27.  365  by  1200 


124  FOUKTH  YEAH  [Oral 

DIVISORS   ENDING   IN  NAUGHT 

1.  Divide  60  by  10.  Remove  0  from  60.  60  is  Low 
many  times  6? 

2.  Compare  40  and  4;  30  and  3;  2  x  10  and  20  ^  10. 
What  effect  has  the  removing  of  naught  from  the  right 
of  a  number  upon  the  value  of  the  number? 

3.  Divide  by  10:  20;  900;  350;  470;  530;  260;  740. 

4.  Howmany  are  100x6?  100x9?  600^100=? 
900-^100=?  How  many  naughts  are  removed  from 
the  right  of  900  when  it  is  divided  by  100?  from  the 
right  of  600?  What  effect  has  the  removing  of  two 
naughts  from  the  right  of  a  number  upon  the  value  of 
the  number  ? 

5.  Find  1000x9;  1000x3;  9000^1000;  3000-^ 
1000.  How  many  naughts  are  removed  from  the  riglit 
of  9000  when  it  is  divided  by  1000  ?  from  the  right  of 
3000  ?  What  effect  has  the  removing  of  three  naughts 
from  the  right  of  a  number  upon  the  number  ? 

Removing  one  naught  from  the  right  of  a  number 
divides  the  number  hy  10;  removing  tivo  naughts,  divides 
it  hy  100 ;  removing  three  naughts,  divides  it  hy  1000,  etc. 

Find  quotients : 

6.  30^10  10.  300^100  14.  4000^100 

7.  90-^10  11.  600 -^  100  15.  5000^1000 

8.  70^10  12.  700 -^  100  16.  9000-^1000 

9.  200-^10        13.   900 -f- 100  17.    7000 -f- 1000 


Oral  and  Written]  DIVISION  125 

1.  Divide  1460  by  20. 

2^)146^  Cutting   off    naught,   or   the    same 

73  number  of  naughts,  from  hoth  dividend 

2iS)i^)146(J^  and  divisor  does  not  change  the  quo- 

"~73  tient. 

Find  the  quotients : 

2.  80-^-20        6.     900^100  10.  12000^1000 

3.  60-^30        7.   1000-^100  11.  12000^2000 

4.  90^-10        8.   6000^200  12.  18000^3000 

5.  40-^20        9.   8400^400  13.  16000^4000 

14.  How  many  10-gallon  cans  will  a  dealer  use  in 
shipping  200  gallons  of  milk  ? 

15.  How  many  20-lb.  packages  can  be  made  from 
1000  lb.  of  coffee  ? 

16.  2000  pounds  of  crackers  were  shipped  in  400 
boxes.     How  many  poimds  did  each  box  contain  ? 

17.  How  many  $20  coats  must  be  sold  to  realize 
$2400? 

18.  A  man  bought  a  house  for  $3500.     How  many 
months  will  it  take  to  pay  for  it  at  $100  a  month  ? 

Give  quotients  at  sight : 

19.  160-^40  24.   200 

20.  360^30  25.    480 

21.  900^90  26.   480 

22.  750-^30  27.   220 

23.  850-^50  28.   240 


50 

29. 

750-4-  15 

80 

30. 

300^  60 

60 

31. 

250^  25 

110 

32. 

600-4-  50 

120 

33. 

700  +  140 

126 


FOURTH   YEAR 


[Written 


MULTIPLICATION  BY  TWO-FIGURE  NUMBERS 


1.   Multiply  64  by  23. 


Multiplicand 

64 

64 

Multiplier 

23 

23 

1st  partial  product 

192=   3x64 

192 

2d  partial  product 

1280  =  20x64 

128 

Entire  product 

1472  =  28x64 

1472 

In  practice  the  0  in  the  second  partial  product  is 
omitted,  and  1280  is  written  as  128  tens  by  placing 
the  right-hand  figure  of  that  product  in  tens'  place. 


2. 

3. 

4. 

5. 

327 

203 

6004 

3060 

35 

42 

73 

89 

1635 

406 

18012 

27540 

981 

812 

42028 

24480 

11445 

8526 

438292 

272340 

Multiply : 

a 

6 

c 

d 

e 

6.     63 

645 

863 

765 

806 

24 

32 

24 

35 

43 

7.     98 

346 

609 

963 

863 

23 

54 

15 

41 

51 

8.   604 

861 

867 

763 

867 

43 

32 

45 

54 

36 

Written]  MULTIPLICATION  127 

Multiply : 

1.  426  by  23  ii.  634  by  37  21.  9006  by  48 

2.  372  by  41  12.  298  by  73  22.  2694  by  75 

3.  256  by  33  13.  604  by  48  23.  8002  by  38 

4.  307  by  32  i*.  729  by  40  24.  4293  by  67 

5.  269  by  43  15.  903  by  86  25.  9128  by  39 

6.  307  by  27  le.  694  by  79  26.  2807  by  74 

7.  538  by  36  17.  928  by  89  27.  6293  by  56 

8.  736  by  63  '  is.  726  by  75  28.  4060  by  13 

9.  487  by  52  19.  349  by  28  29.  2734  by  27 
10.  994  by  35  20.  723  by  14  30.  4169  by  32 

31.  Announce  products  at  sight : 

50x90        90x70        20x80  70x60  70x40 

80x70         60x50        40x30  30x30  90x90 

3x3  =  9;  9  is  the  square  of  3.  6  x  6  =  36 ;  36  is  the 
square  of  6. 

To  find  the  square  of  a  numher,  we  multiply  it  by  itself. 

32.  Find  the  squares  and  memorize  : 

2,  3,  4,  5,  6,  7,  8,  9,  10,  11,  12,  13,  14,  15,  16,  17,  18, 
19,  20,  21,  22,  23,  24,  25. 

Multiply : 

33.  463  by  73  37.  9869  by  84  4i.  8693  by  28". 

34.  938  by  84  38.  3278  by  93  42.  9281  by  39 

35.  697  by  95  39.  9009  by  49  43.  7375  by  47 

36.  893  by  96  40,  6075  by  74  44,  4069  by  §9 


128  FOURTH  YEAR  [Written 

MULTIPLICATION   OF   CONCRETE   NUMBERS 

Which  of  the  following  numbers  are  abstract  f  Which 
are  concrete  f     Why  ? 

1.  8  ;  6  days ;   $  4 ;  5^ ;  25  ;  4  feet ;  8  horses. 

2.  Name  the  multiplier  and  the  multiplicand  in  each 
problem  : 

$  8  64  days  81  horses  72  oranges 

X  5  X  4  .   2<_7  X  3 

3.  Observe  in  each  of  the  above,  problems  that  the 
product  must  have  the  same  name  as  the  multiplicand. 

The  multiplier  is  always  an  abstract  7iiimber. 

4.  When  two  numbers  are  multiplied,  the  number  in 
the  product  remains  the  same  in  whatever  order  the 
numbers  are  taken;  thus:  7  x  12  =  12  x  7. 

5.  How  much  do  I  earn  in  125  days  at  $  3  per  day  ? 
In  problems  like  this  where  the  multiplier  has  more 

figures  than  the  multiplicand,  the  product  of  the  num- 
bers may  be  found  thus :  125,  but  the  analysis  of  the 

3 
375 
problem  should  be  given  in  this  way : 
I  earn  in  one  day,  $3. 
I  earn  in  125  days,  125  x  $3,  or  $375. 

Find  the  cost  of  :  How  many  : 

6.  319  days'  work  @  $  3  lo.   Pints  in  327  qt.  ? 

7.  817  tons  coal  @  $  5  ii.  Inches  in  845  ft.  ? 

8.  198  lb.  meal  @  9f^  12.   Pecks  in  164  bu.  ? 

9.  345  doz.  buttons  @  S^  13.   Ounces  in  375  lb.  ? 


Written]  MULTIPLICATION"  129 

PRACTICAL   PROBLEMS 

Find  the  cost  of : 

1.  28  pounds  of  raisins 

2.  46 J  gallons  of  vinegar 

3.  196  pounds  of  sugar 

4.  48 J^  pounds  ol  butter 

5.  64.1^  pounds  of  meat 
.  6.  85  dozen  oranges 

7.  27  gallons  of  molasses 

8.  58^  bushels  of  potatoes 

9.  25  dozen  eggs 

10.  54  barrels  of  flour 

11.  27  barrels  of  apples 

12.  34  tons  of  coal 

13.  148 J  pounds  of  tea 

14.  144  dozen  eggs 

15.  48  yards  of  cloth 

16.  36 J  tons  of  hay 

17.  The  frontage  on  a  city  street  is  176  feet.  How- 
much  is  it  worth  at  $  65  a  front  foot  ? 

18.  A  grocer  sold  18  firkins  of  butter,  each  contain- 
ing 56  pounds,  at  24^  a  pound.  How  much  did  he 
receive  for  the  butter  ? 

19.  A  boy  works  8  hours  a  day.  How  many  hours 
does  he  work  in  28}  days  ? 


@ 

15^. 

@ 

24^. 

@ 

6^. 

@ 

27^. 

@ 

16^. 

@ 

35)^. 

@ 

48^. 

@ 

60  A 

@ 

23^. 

@ 

$5.25. 

@ 

$2.35. 

@ 

$  6.75. 

@ 

50  >^. 

@ 

26  (^. 

@ 

87^. 

@  $16.70. 

130  FOURTH  YEAR       [Oral  and  Written 

COMPARISON 

In  the  following  comparisons  the  first  number  is  to 
be  divided  by  the  second: 

1.  Compare  12  and  4 ;  12  and  3  ;  16  and  4. 

2.  Compare  5  and  15. 

3.  Compare : 

18  and  6  16  and  4 .  6  and  12. 

20  and  5  45  and  9  6  and  30. 

4.  When  3  oranges  cost  10  cents,  how  much  will  12 
oranges  cost  ? 

Note.  — 12  oranges  equal  4x3  oranges ;  hence  they  will  cost 
4  X  10  cents,  or  40  cents. 

5.  At  6  melons  for  25  cents,  how  much  will  24  cost  ? 

6.  At  12  lemons  for  15  cents,  how  much  will  72  cost  ? 

7.  If  8  tons  of  coal  cost  $54,  how  much  will  40  tons 
cost  ? 

8.  If  3  collars  cost  35  cents,  how  much  will  24  collars 
cost? 

9.  When  12  cords  of  wood  cost  $48,  how  much  will 
3  cords  cost  ? 

10.  How  much  will  4  qt.  of  milk  cost  when  16  qt. 
cost  $1.28? 

11.  When  7  tons  of  hay  sell  for  $91,  how  much  will 
a  farmer  receive  for  35  tons  ? 

12.  If  96  acres  of  land  are  worth  $2592,  how  much 
are  12  acres  worth  ? 


f 

I  Oral] 


DIVISION 


131 


REVIEW  OF  SHORT  DIVISION 

Answer  at  sight : 

1.  2}32  3}48  4)44         5)35  5)75 

2.  6^  7)147         8)872       9)3699     8)4056 


Give  answers  quickly 


3.  1  of    16 

4.  1  of    24 

5.  1  of    48 

6.  I-  of    60 

7.  1  of    72 

8.  i  of    84 

9.  I  of    96 

10.  1  of  108 

11.  3-VoflOO 


12. 


Ir  of  132 


TT 


13.  iVofl44 

Divide  and  test : 

14.  11)6303         11)2244 


;  18 

;  26 

;  28 

;   32 

;   36; 

;  27 

;  36 

;  18 

;   60 

,   90; 

;  24 

60 

;  72 

;   36 

,   44; 

;  55; 

100, 

150; 

75; 

45; 

;  96; 

84; 

24; 

48; 

240; 

;  91 

;  49 

63 

;  105 

;  350; 

;  72 

,  640 

;  960 

;  560 

;  120; 

;  135 

,  360 

;  720 

;   54 

;  7209; 

;  120, 

130 

,  190 

;  1250 

,  1950; 

;  88, 

09, 

77 

,  1100, 

1320; 

;  288; 

96. 

84 

;  960. 

,  840; 

40. 
120. 

56. 

65. 

36. 
2100. 
880. 
1080. 
1780. 
1210. 
1080. 


11)2882  11)6699 


15.   12)96840       12)89640         12)6072  12)9060 


Give  quotients  at  sight : 

8)96         9)72         10)190 


16 


11)121 


12)96, 


132  '  FOURTH  YEAR  [Written 

LONG  DIVISION 
1.   Divide  240  by  15. 

16  Quotient.  In  long  division  tlie  quotient 

Divisor  15)240  Dividend,     is  placed  over  the  dividend.    15 

15  is    contained    in    24,    1   time. 

90  Write   the    1   in  the  quotient 

90  over  the  4.     Multiply  15  by  1, 

0  placing  the  product,  15,  under 

24.     Subtract  15  from  24.    The  remainder  is  9.    Bring 

down  the  next  figure,  0.     15  is  contained  in  90,  6  times. 

Multiply  15  by  6,  placing  the  product,  90,  under  90.  As 

there  is  no  remainder,  the  quotient  is  IG. 

Divide : 


21  Ans. 

23  Ans.                        209  Ans, 

2.  13)273 

3.  14)322             4.  25)5225 

26 

28                         50 

13 

42                         225 

13 

42                        225 

5.   How  many 

times  is  21  contained  in  504  ? 

24 

Steps : 

L)504 

1.   Divide  50  by  21. 

42 

2.   Write  quotient  figure. 

«4 

3.   Multiply  21  by  2. 

■M 

4.   Subtract  42  from  50. 

5.    Bring  down  next  figure. 

Test.  — 24x21  =  504. 

6.    Divide  441 

by  21 ;  672  by  21 ;  903  by  21. 

Written]  DIVISION  133 

FINDING   THE   QUOTIENT   FIGURE   IN  DIVISION 

Think  how  many  times  the  first  figure  of  the  divisor 
is  contained  in  the  first  figure  of  the  dividend.  The 
number  will  be  the  first  figure  of  the  quotient. 

1.  252-^21  4.   714 -f- 21  7.     504-^21 

2.  525-^21  5.   651-^21  8.   2398^21 

3.  861 H- 21  6.   357^21  9.   2625^21 
Think  how  many  times  the  first  figure  of  the  divisor 

is  contained  in  the  first  figure,  or  in  the  first  two  figures, 

of  the  dividend.     The  number  will  be  the  first  figure 
of  the  quotient. 

7061^23  18.   6831 -^  33 

9269^23  19.    1984^32 

5028-^42  20.   2272^32 

1344^42  21.    1683^51 

22.  Divide  819  by  21. 

.  .  39 

Since  the  product  of  the  divisor 

and  quotient  is  greater  than  81,  the         ^ 

^  quotient  figure  is  too  large.     Try  a  y— 

—       smaller  quotient  figure. 

189 

23.  Divide  651  by  21. 

2  .  -^ 

o-j  YprT         Since  the  remainder  is  greater  than     21) 651 

.0       the  divisor,  the  quotient  figure  is  too  63 

00       small.     Try  a  larger  quotient  figure.  21 

21 


10. 

713^31 

14. 

11. 

899-^31 

15. 

12. 

6727-^31 

16. 

13. 

8323-^41 

17. 

134 

FOUKTH   YEAR 

[Written 

Divide  and  tesi 

1  \ 

1.   21)882 

13. 

23)575 

25. 

33)462 

37. 

43)1333 

2.   21)903 

14. 

23)736 

26. 

33;  858 

38. 

43)6880 

3.   21)504 

15. 

23)966 

27. 

33)561 

39. 

43)9460 

4.   21)819 

16. 

23)138 

28. 

33)627 

40. 

43)1376 

5.   21)315 

17. 

31)775 

29. 

41)943 

41. 

51)1683 

6.   21)567 

18. 

31)744 

30. 

41)2296 

42. 

51)3672 

7.   21)399 

19. 

31)899 

31. 

41)1107 

43. 

51)3264 

8.   21)441 

20. 

31)217 

32. 

41)1435 

44. 

51)1428 

9.   22)814 

21. 

32)672 

33. 

42)1008 

45. 

52)1508 

10.   22)638 

22. 

32)928 

34. 

42)1596 

46. 

52)2288 

11.   22)352 

23. 

32)160 

35. 

42)1680 

47. 

53)2385 

12.   22)660 

24. 

32)192 

36. 

42)1722 

48. 

53)1908 

49.  A  butcher  paid   $1476  for  41  head  of   cattle. 
How  much  was  that  per  head? 

50.  If  a  railroad  trackman  walks  16  miles  each  day, 
how  long  will  he  be  in  walking  832  miles  ? 

51.  If  there  are  496  ounces  in  31  pounds,  how  many 
ounces  are  there  in  1  pound  ? 

52.  If  24  barrels  of  oil  cost  $  44.40,  what  is  the  price 
of  1  barrel  ? 

53.  If  a  bushel  of  oats  weighs  32  lb.,  how  many 
bushels  will  weigh  28640  lb.  ? 

54.  How  long  will  it  take  a  train  that  travels   35 
miles  an  hour  to  go  a  distance  of  315  miles  ? 

55.  At  38  ^  a  word,  how  many  words  can  I  cable  from 
New  York  to  Sweden  for  $3.04? 


Written] 

DIVISIOK 

135 

LONG  DIVISION 

1.   Divide  7416  by 

25. 

29616 

Quotient            Write   the  remainder 

25)7416 

over    i 

the 

divisor,    and 

50 

annex 

it   to    the   right 

241 

of  the 

quotient. 

225 

Test 

296  X  25  = 

166 

7400; 

7400 

+  16  =  7416. 

150 

16  remainder -^  25  =  J|-. 

Divide  and  test : 

• 

2. 

2397  by  51 

13. 

1281  by  21 

24. 

6938  by  94 

3. 

3888  by  86 

14. 

1703  by  27 

25. 

7159  by  39 

4. 

1302  by  21 

15. 

3034  by  46 

26. 

8697  by  28 

5. 

2945  by  38 

16. 

4697  by  61 

27. 

4910  by  45 

6. 

3213  by  51 

17. 

4368  by  98 

28. 

3682  by  73 

7. 

1827  by  27 

18. 

4544  by  76 

29. 

4918  by  94 

8. 

3007  by  36 

19. 

2867  by  61 

30. 

8168  by  86 

9. 

6256  by  81 

20. 

2058  by  27 

31. 

7369  by  69 

10. 

5096  by  95 

21. 

2668  by  31 

32. 

8925  by  28 

11. 

2542  by  41 

22. 

3592  by  43 

33. 

8010  by  65 

12. 

3567  by  87 

23. 

2047  by  83 

34. 

9102  by  98 

35.  How  many  suits,  at  $32  each,  can  be  bought  for 
$1095,  and  what  amount  will  be  left  ? 

36.  Find  the  number  of  barrels  of  oil,  51  gallons  each, 
that  can  be  filled  from  a  vessel  containing  408  gallons. 


136  FOURTH  YEAR  [Written 

PRACTICAL  PROBLEMS 

1.  At  $.25  each,  how  many  books  can  you  buy  for 
$6.25? 

$6.25  =  625^  $.25  =  25^ 

2o      No.  of  books. 
Cost  of  1  book  25  ^)  625  ^  money  spent. 
50 

125 
125 

2.  At  16  cents  each,  how  many  belts  can  be  bought 
for  $4.80? 

3.  Mary  paid  24  cents  a  pound  for  butter.  The 
amount  of  her  bill  was  $3.12.  How  many  pounds  did 
she  buy  ? 

4.  How  many  gallons  equal  652  quarts  ? 

5.  I  bought  silk  at  75  cents  a  yard  and  paid  $13.50. 
How  many  yards  did  I  buy  ? 

6.  In  how  many  months  will  a  man  save  $1120,  if 
he  saves  $32  a  month  ?  in  how  many  years? 

7.  How  many  bars  of  iron,  weighing  56  lb.  each,  are 
equal  in  weight  to  a  bar  weighing  18200  lb.  ? 

8.  A  man  sold  land  for  $45  an  acre,  receiving 
$7200  for  it.     How  many  acres  did  he  sell? 

9.  An  orchard  contains  4032  trees,  planted  in  32 
rows.     How  many  trees  are  there  in  a  row  ? 

10.    A  farm  of  174  acres  was  sold  for  $12970.    What 
was  the  selling  price  per  acre  ? 


Oral  and  Written]     DIVISION  AND  PARTITION  137 

DIVISION  AND  PARTITION 

Division  is  the  process  of  finding  how  many  times  one 
number  contains  another,  or  of  separating  a  number  into 
equal  parts. 

1.  How  many  times  is  $  3  contained  in  $  15  ? 

This  problem  gives  the  size  of  the  equal  parts  ($3) 
into  which  the  dividend  ($15)  is  to  be  divided,  and 
asks  for  the  number  of  equal  parts.  $15-^-$3  =  5,  the 
numher  of  equal  parts. 

2.  What  is  the  quotient  of  $  15  divided  by  3  ? 

This  problem  gives  the  numher  of  equal  parts  (3)  into 
which  the  dividend  ($15)  is  to  be  divided,  and  asks  for 
the  size  of  each  part.  |  of  $  15=  $  5,  the  size  of  each 
part.     This  kind  of  division  is  called  partition. 

First  state  whether  each  problem  calls  for  the  numher 
of  equal  parts  or  the  size  of  each  part,  and  then  give 
answers : 

3.  144  in.  -^  12  in.  7.    192  bu.  ^  16  bu. 

4.  125  yd.  ^5  8.    108  in. -^9 

5.  $132^  $11  9.   ^oi  $250 

6.  150  ft.  -f- 10  10.   i  of  128  da. 

11.  At  45^  a  bushel,  how  many  bushels  of  com  will 
sell  for  $17.55? 

12  If  28  Stanhope  buggies  are  sold  for  $  2912,  what 
is  the  average  price  ? 

13.  If  a  train  runs  1036  miles  in  37  hours,  how  far 
will  it  run  in  one  hour  ? 


138 


FOURTH  YEAR 


[Written 


REVIEW 

Find  the  cost  of: 

1.  131  lb.  of  butter  at  25^  a  lb. 

2.  64  suits  at  $81  each. 

3.  32  pairs  of  shoes  at  $2  a  pair. 

4.  400  lb.  of  sugar  at  4^  a  pound. 

5.  36  overcoats  at  $13.25  each. 

6.  3000  envelopes  at  $12  a  thousand. 

7.  172  yards  of  cloth  at  87^  a  yard. 

8.  2500  lb.  of  coffee  at  20/  a  pound. 

9.  128  hogs  at  $161  each. 

10.  37  hats  at  $2.25  each. 

11.  451  yards  of  silk  at  80/  a  yard. 

12.  1  gross  pencils  at  60/  a  dozen. 

13.  32  cows  at  $32  each. 

14.  125  tons  of  hay  at  $14.75  a  ton. 

15.  72  bbl.  of  flour  at  $5.25  a  barrel. 

16.  14  bolts  of  ribbon  at  75/  a  bolt. 

17.  78  bu.  of  wheao  at  87/  a  bushel. 

18.  47|  bu.  of  oats  at  40/  a  bushel. 

19.  25  bu.  of  corn  at  50/  a  bushel. 

20.  25  lb.  of  meat  at  25/  a  pound. 

21.  21  doz.  pairs  of  gloves  at  $1  a  pair. 

22.  36 J  yd.  of  cloth  at  18/  a  yard. 

23.  2  gross  penholders  at  50/  a  dozen. 


Add; 

24. 


25. 


26. 


27. 


$463.75 
695.42 

1937.86 
947.75 
678.93 

$6937.85 
596.27 

8346.39 
326.42 

2186.75 
495.38 

$9612.73 
693.85 

2928.46 
478.74 

8569.93 
195.84 

$3762.95 

661.43 

99.87 

875.67 

989.86 

4987.19 


Written]  PRACTICAL   WORK  139 

PRACTICAL  WORK 

Market  Report 

Potatoes,  75^  per  bu.  Corn,  46^  per  bu. 

Beans,  .$1.25  per  bu.  Baked  beans,  95^  per  doz.  cans. 

Butter,     Print,38^  per  lb.  Celery,  25^  per  doz. 

Dairy,  25^  per  lb.  Eggplant,  75^  per  doz. 

Sugar,  100  lb.  bag,  $5.50.  Watercress,  40  f  per  doz. 

Flour,  per  bbl.,  $5.80.  Blackberries,  per  crate,  $3.20. 

From  the  market  report  find  the  cost  of  each  of  the 
following : 


1. 

7  bu.  potatoes. 

7. 

8  bu.  corn. 

2. 

15  lb.  prmt  butter. 

8. 

10  bags  sugar. 

3. 

12  doz.  celery. 

9. 

25  bbl.  flour. 

4. 

25  doz.  watercress. 

10. 

2  doz.  cans  baked  beans. 

5. 

5  bu.  beans. 

11. 

7  doz.  eggplant. 

6. 

12  lb.  dairy  butter. 

12. 

3  crates  blackberries. 

J 

^.t  121  ^  each  find  the  cost  of : 

13. 

72  lb.  of  meat. 

18. 

176  cards  of  buttons. 

14. 

144  books. 

19. 

272  pecks  of  potatoes. 

15. 

64  vases. 

20. 

128  baskets  of  tomatoes. 

16. 

168  cups. 

21. 

96  watermelons. 

17. 

256  yd.  of  lawn. 

22. 

152  yd.  of  ribbon. 

23.  If  it  is  8  miles  from  A  to  B,  and  4^  times  as  far 
from  B  to  C,  how  far  is  it  from  A  to  C  ? 

24.  James  bought  10  lb.  of  sugar  at  5  J  cents  a  pound ; 
41  lb.  of  butter  at  20  cents  a  pound ;  6  lemons  at  3  for 
5  cents ;  and  two  8-cent  loaves  of  bread.  He  gave  the  gro- 
cer a  two-dollar  bill.     How  much  change  did  he  receive? 


140  rOUETH  YEAR  [Written 

PRACTICAL   PROBLEMS 

1.  A  farmer  has  28  cows  in  three  fields.  If  there 
are  12  in  the  first,  and  9  in  the  second,  how  many  cows 
are  there  in  the  third  field  ? 

2.  The  farmer  values  his  cows  at  an  average  of  $  35 
each.     What  is  the  value  of  all  ? 

3.  The  fields  over  which  they  graze  contain  24  acres, 
18  acres,  and  14  acres.  How  much  grazing  land  is  there, 
and  what  is  the  value  of  this  land  at  $  35|-  an  acre  ? 

4.  If  the  farmer  receives  21560  gallons  of  milk  a 
year,  how  much  is  it  worth  at  1 2  cents  a  gallon  ? 

5.  His  Jersey  cow  yields  350  lb.  of  butter  a  year, 
which  he  sells  at  28  cents  a  pound.  How  much  does  he 
receive  for  it  ? 

6.  He  sold  5  of  the  cows  at  an  average  price  of 
$  48.50.     How  much  did  he  receive  for  them  ? 

7.  He  keeps  2  men  at  $  22 J  a  month,  to  work  on 
the  farm.     How  nnich  does  the  labor  for  the  year  cost  ? 

8.  He  sold  14  calves  for  $  98.  How  much  did  he 
receive,  on  an  average,  for  each  ? 

9.  His  grocery  bill  averaged  $  36J  per  month.  Find 
his  bill  for  the  year. 

10.  He  purchased  2  horses,  one  at  $  125,  and  one  at 
$  150 ;  and  2  wagons  at  $  85  each.  Repairs  on  the 
farm  cost  $  87.50.     Find  the  amount  paid. 

11.  He  bought  1^  doz.  milk  cans  at  $1.25  each. 
How  much  did  they  cost  ? 


Oral  and  Written] 


MEASURES 


141 


MEASURES   OF   TIME 

1.  Write  the  days  of  the  week 
and  the  months  of  the  year,  with  their 
abbreviations. 

2.  Observe  that  the  second  hand 
moves  over  60  small  or  second  spaces, 
while  the  minute  hand  moves  over 
one  minute  space. 

3.  Memorize  this  table  : 


60  seconds  ( 

sec.)  =  1  minute 

(min.) 

60  minutes  = 

=  1  hour  (hr.) 

24  hours  =  1 

day  (da.) 

365  days  =  l 

year  (yr.) 

September,  November,  April,  and  June  have  each 
30  days.  All  the  others  except  February  have  31  days 
each.  February  usually  has  28  days.  A  year  that 
has  366  days  is  called  a  leap  year.  In  leap  year 
February  has  29  days. 


4.    Memorize  this  rhyme : 
Thirty  days  have  September, 
April,  June,  and  November. 
All  the  rest  have  thirty-one, 
Save  February,  which  alone 
Has  twenty-eight ;  and  one  day  more 
We  add  to  it  one  year  in  four. 


Change : 

5.  3  min.  to  sec. 

6.  6  da.  to  hours. 

7.  7  hr.  to  minutes. 

8.  3  da.  6  hr.  to  hr. 

9.  10  wk.  6  da.  to  da. 


10.    How  many  days  are  there   in  April,  May,  and 
June  ?  in  November,  December,  and  January  ? 


142 


FOURTH  YEAR        [Oral  and  Written 


MEASURES   OF   WEIGHT 

1.  Name  some  arti- 
cles bought  by  the  ounce 
(oz.) ;  by  the  pound. 

2.  How  many  ounces 
are  there  in  1  pound  ?  in 
10  pounds  ? 

Coal,  hay,  sand,  plas- 
ter, etc.,  in  large  quanti- 
ties, are  sold  by  the  ton 
of  2000  pounds. 

3.  Memorize  the  table : 


16  oz.  =  1  pound  (lb.) 
2000  pounds  =  1  ton  (T.) 


4.  A  dealer  buys  150  bales  of  hay,  averaging  90 
pounds  to  the  bale.  How  many  tons  and  pounds  over 
does  he  buy  ? 

5.  At  3  cents  an  ounce,  how  much  will  1  pound  of 
mustard  cost  ? 

6.  Find  the  cost  of  six  kegs  of  nails,  each  keg  weigh- 
ing 100  lb.,  at  5|-  cents  a  pound. 

7.  2  tons  of  rolled  oats  were  packed  in  pound  pack- 
ages.    How  many  packages  were  there  ? 

8.  How  many  ounces  are  there  in  a  ton  ? 

•  9.   A  load  of  hay  weighed  3000  pounds.     How  many 
tons  did  it  weigh  ?    What  was  its  value  at  $  14  a  ton  ? 


Oral  and  Written]  MEASURES  143 

MEASURES   OF   LENGTH   OR  DISTANCE 

1.  Name  the  measures  that  you  have  already  learned. 

2.  A  foot  =  inches. 

3.  A  yard  =  feet. 

4.  What  measure  should  you  use  to  measure  the 
length  of  your  book  ?  of  your  desk  ?  the  width  oi  your 
schoolroom  ?    the  length  of  the  blackboard  ? 

5.  Measure  b^  yards  or  W^  feet  along  the  street  or 
on  the  school  ground.     Call  it  one  rod. 

6.  Secure  a  tape  measure  5|  yards  long,  and  with 
it  measure  the  length  and  the  width  of  your  school 
grounds  in  yards  and  feet. 

7.  With  a  pole  or  a  tape,  a  rod  in  length,  measure  the 
distance  in  rods  and  feet  around  a  square  or  a  field. 

8.  20  city  blocks,  each  16  rods  in  length,  are  320 
rods  long.     This  is  called  one  mile.     1  mile  =  320  rods. 

9.  320  X  161  ft.  =  feet.  (Why  do  we  multi- 
ply 16|  ft.  by  320  ?) 

10.  5280  ft.  ^  3  =  yards.      (Why  do  we  divide 

5280  ft.  by  3  ?) 

11.  Memorize  this  table : 


12 

inches 

(in.)  =  1  foot  (ft.) 

3 

feet 

=  1  yard  (yd.) 

5l  yards, 

or  161  feet 

=  1  rod  (rd.) 

320 

rods 

=  1  mile  (mi.) 

1760  yards 

5  =  1 

mile 

5280  feet  =  1  mile 

144  FOURTH  YEAR  [Oral 

MEASURES   OF   LENGTH   OR  DISTANCE 

Change : 

1.  60  ft.  to  yd.  7.  5  ft.  to  in. 

2.  27  rd.  to  ft.  8.  120  in.  to  ft. 

3.  16  ft.  to  in.  9.  72  ft.  to  yd. 

4.  42  in.  to  ft.  10.  420  in.  to  ft. 

5.  320  rd.  to  ft.  11.  1250  yd.  to  ft. 

6.  1760  yd.  to  ft.  12.  120  rd.  to  ft. 

13.  How  many  feet  of  fence  are  required  for  a  garden 
in  the  form  of  an  oblong  26  yards  long  and  12  yards 
wide  ? 

14.  James  lives  180  rods  from  the  schoolhouse.  How 
many  feet  does  he  travel  in  going  to  and  coming  from 
school  each  day  ? 

15.  A  boy  travels  135  yards  each  day  in  carrying  the 
mail.  How  many  yards  does  he  travel  in  6  days? 
How  much  less  than  a  mile  does  he  travel? 

MEASURES   OF   SURFACE 

1.  Draw  a  square  inch.  What  two  things  show 
that  it  is  a  square  inch  ? 

2.  Draw  on  the  blackboard  one  square  foot.  What 
two  things  show  that  it  is  a  square  foot  ? 

3.  Separate  each  side  of  a  square  foot  into  12  equal 
parts.  Connect  these  points  by  straight  lines.  What 
is  the  size  of  each  square  ?  the  name  of  each  square  ? 
How  many  square  inches  equal  one  square  foot  ? 


Oral] 


MEASURES 


145 


144  square  inches  =  1  square  foot 


4.  Draw  on  the  blackboard  a  square  yard.      What 
two  things  show  that  it  is  a  square  yard  ? 

Let  one  inch  represent  a  foot.     How  long,  then,  is 
the  side  of  the  square  that  represents  a  square  yard? 

5.  Represent  a  square  yard  by  a  square,  each  side 
of  which  is  f  inch.  Then,  \  inch  represents  1  foot. 
How  long  is  each  side  of  a  square  yard  ? 
Measure  the  surface  of  the  square  yard  by 
1  square  foot.  How  many  square  feet  are 
there  in  the  upper  row  ?  in  the  second  row? 
in  the  three  rows  ? 


w, 

9  sq.  ft.  =  1  sq.  yd. 


^^/S- 

6.  This  drawing  represents 
an  oblong  4  yards  long  and  2 
yards  wide.  Measure  the  sur- 
face by  1  square  yard.  How 
many  square  yards  are  in  one 
row  ?    in  both  rows  ? 

In  1  row  there  are  4  sq.  yd. 

In  2  rows  there  are  2  x  4  sq.  yd.  or  8  square  yards. 

7.  How  many  square  yards  are  there  in  an  oblong 
5  yd.  long  and  4  yd.  wide  ? 

The  number  of  square  inches,  square  feet,  or  square 
yards  a  surface  contains  is  called  its  area. 


146  FOURTH  YEAR  [Written 

MEASURES    OF    SURFACE 

Find  the  area  in  square  inches  of: 

1.  An  oblong  6  in.  by  4  in.      5.   An  8-in.  square 

2.  A  square  7  in.  on  each  side.    6.    A  12-in.  square 

3.  A  page  8  in.  by  5  in.  7.    A  9-in.  square. 

4.  A  slate  10  in.  by  12  in.       8.    A  10-in.  square. 
9.    Draw  a  figure  to  represent  an  oblong  5  in.  long 

and   3    in.    wide.     Find   its   area.     Find   the   distance 
around  the  oblong. 

The  distance  around  a  figure  is  called  the  perimeter. 

10.  Find  the  perimeter,  iii  inches,  of  each  figure  de- 
scribed in  problems  1  to  9. 

Represent  the  following  figures  by  a  scale  of  1  inch  to 
the  foot,  and  find  the  area  and  the  perimeter : 

11.  A  6-ft.  square.  i3.    A  wall  9  ft.  by  6  ft. 

12.  A  rug  9  ft.  by  4  ft.       i4.   A  table  6  ft.  by  5  ft. 

Find  the  area  and  the  perimeter.  Represent  on  a 
scale  of  1  inch  to  a  yard : 

15.  A  schoolroom  10  yd.  long  and  8  yd.  wide. 

16.  A  hall  15  yd.  long  and  3  yd.  wide. 

17.  A  sidewalk  12  yd.  long  and  2  yd.  wide. 

18.  Matting  for  a  room  5  yd.  long  and  4  yd.  wide. 

19.  Measure,  in  even  yards,  the  length  and  width  of 
your  schoolroom  floor,  and  draw  the  figure  on  a  scale 
of  1  in.  to  the  yard  3  1  in.  to  the  foot. 


Oral,  Written]    READING  AND  WRITING  NUMBERS     14T 


READING   AND  WRITING   NUMBERS 

1.  How  are  large  numbers  pointed  off  before  being 
read? 

2.  Name  the  periods  of  numbers  up  to  millions. 

3.  Read  2,028,375.  Notice  that  in  reading  a  num- 
ber the  units'  period  is  not  named.  Thus  this  number 
is  read  2  millioriy  28  thousa7id,  375;  no ^375  units. 

The  next  period  after  millions  is  called  billions*  period. 
Copy,  point  off,  and  read: 
a 

4.  2405 

5.  3065 

6.  7005 

7.  8900 

8.  6666 

9.  3050 

10.  9580 
Write : 

11.  Six  thousand  six  hundred  six. 

12.  Two  billion  ten  million  four. 

13.  Seventy-five  thousand  nine  hundred  six. 

14.  One  billion  eight  million  seventy-five. 

15.  Eighty-four  million  six  hundred  five  thousand. 
Twenty-five  thousand  thirty-eight. 
Nine  hundred  million  nine  hundred  ninety-nine. 
Two  million  six  thousand  thirty. 


b 

c 

d 

30670 

6800907 

8645742689 

49007 

400745 

750680009 

40074 

8790007 

406009807 

87090 

4057042 

6804704924 

90703 

3012890 

9000000250 

65002 

7000002 

8057000000 

73200 

9050601 

5700809563 

16. 
17. 
18. 
19. 


One  billion  one  million  one  thousand. 


148  FOUKTH  YEAR  [Written 

REVIEW 


1.   Begin  with  9  and  count  by  9's  to  126.    23.  2.  2134 

2.    Begin  with  1  and  count  by  9's  to  118. 

s.  2124 

Add  by  columns  and  by  lines : 

4.  2110 

a        b 

c                           d         e        f 

6.  2124 

3. 

42  +  74  +  39=         8.   24  +  32  +  65  = 

6.  2124 

4. 

36  +  93  +  61=          9.   39+86  +  92  = 

7.  2064 

5. 

27  +  81  +  87=        10.   94  +  39  +  19=     . 

9.  2123 

€. 

49  +  64  + 

49=        11.   28  +  76  +  85  = 

10.  2128 

7. 

38  +  72  + 

86=        12.   63  +  15  +  84  = 

11.  2124 

+      + 

=                   +      +      = 

12.  2109 

a 

6                   c               d 

13.  2114 

13. 

$42.35+^ 

$24.63 +  $36.74 +  $82.95  = 

U>  2063 

14. 

18.69  + 

32.78+      6.27+      2.39  = 

16.  2110 

15. 

2.41  + 

41.65+        .96+    49.85  = 

17.  2124 

16. 

36.74  + 

59.83+    18.49+    13.74  = 

18.  2124 

17. 

8389  + 

43.62+      9.37+    26.48  = 

19.  2124 

20.  2124 

21.  2062 

+ 

+             +              = 

18. 

$57.35  + 

$75.15+  $72.26+  $275.25  = 

23.  2128 

19. 

63.27  + 

64.23+      17.83+     375.65  = 

24.  2124 

20. 

54.86  + 

81.37+     27.64+     825.45  = 

25.  2124 

21. 

83.74  + 

76.45+     36.21+     963.75  = 

26.  2124 

22. 

83.64  + 

22.68+      73.56+     856.87  = 

27.  2124 

+ 

+               +                 = 

28.  2058 

23.   From  the  numbers  at  the  right  repre- 

1  tin  DC   thp  rJa.ilv  p.iro.nla.tinn  of   a  r>;q,Tipr-  find 

30.  2120 

31.  2127 

its  circulation  for  July. 


Written]         ADDITION  AND   SUBTRACTION 


149 


BANK  DEPOSITS 


A  bank  is  an  institu- 
tion that  receives  and 
loans  money. 

1.  A  bank  received 
as  follows 
$4126.50 
$2842.35 
$5045.60 
$3862.41 
$6065.70 
$7564.72. 


deposits 

Monday, 

Tuesday, 

\Yednesday, 

Thursday, 

Friday, 

Saturday, 

Find  the  total  deposits 

for  the  week. 

2.  It  paid  out  during 
the  week  $24862.43. 
How  much  more  was  received  than  was  paid  out  ? 

3.  On  June  1,  F.  G.  Bishoff  had  a  balance  on  hand 
of  $4232.44.  During  the  month  he  deposited  $1642.80, 
and  checked  on  his  account  to  the  amount  of  $2214.60. 
What  was  his  balance  in  bank  July  1  ? 

Find  the  balances : 


4. 


Deposits 

Payments 

Deposits 

Payments 

$216443.62 

$111861.74 

5.  $15419.21 

^14000.00 

112384.76 

210987.65 

16987.91 

9044.89 

211129.82 

2940.74 

6456.75 

1055.20 

114781.64 

172.67 

14381.50 

10105.00 

122046.95 

127642.94 

3102.62 

2056.98 

336847.68 

1654.87 

10000.00 

8401.40 

50 

FOURTH 

YEAR 

[Written 

REVIEW   OF 

ADDITION 

Add  (when  written)  4  problems  in  IJ  minutes : 

a 

b 

c 

d 

1.    $751.04 

$146.80 

$345.75 

1187.90 

690.20 

12.96 

187.60 

64.72 

404.72 

842.90 

962.45 

124.87 

812.42 

950.45 

878.72 

671.82 

900.25 

2.75 

964.54 

48.96 

10.48 

24.87 

12.68 

702.84 

2.    $964.77 

$420.41 

$862.41 

$864.12 

844.76 

703.45 

742.87 

246.98 

99.75 

802.60 

368.23 

107.64 

184.65 

12.87 

467.28 

963.66 

209.87 

908.72 

643.82 

478.23 

84.72 

885.88 

782.95 

682.87 

104.88 

225.12 

328.15 

478.24 

84.91 

380.96 

841.62 

332.85 

3.    $844.62       $10642.83        $321.62        $12891.42 
256.48  469.27  41.68  117.68 


741.87 

184.64 

769.62 

49.64 

369.73 

926.48 

186.47 

961.41 

108.42 

12.93 

524.93 

87.83 

957.68 

193.67 

834.71 

113.22 

87.64 

446.72 

221.34 

487.64 

123.96 

689.38 

455.26 

923.06 

p 


Written]  SUBTRACTION  151 

REVIEW   OF    SUBTRACTION 

Write,  subtract,  and  test  4  problems  in  2i-  minutes : 


1. 

a 

$843.87 
632.17 

6 
$376.47 
248.02 

C 

$48892.00 
15079.63 

d 

$2498.73 
519.71 

2. 

$600.01 
289.81 

$246.91 
19.17 

$32171.19 
16693.40 

$7739.82 
7015.09 

3. 

$940.09 
16.41 

$1497.63 
900.75 

$45269.79 
27319.27 

$9999.86 
1305.17 

4. 

$  632.25 
245.19 

$741.20 
523.18 

$37461.27 
19842.07 

$5020.37 
2456.78 

5. 

$  95.33 
49.27 

$61.05 
37.97 

$649.08 
500.16 

$27004.49 
19017.63 

6. 

$82.36 
19.36 

$79.87 
27.93 

$532.98 
403.61 

$75009.75 
69135.92 

7. 

$80.16 
25.31 

$65.32 
13.27 

$763.55 
300.01 

$97382.99 
39853.75 

8. 

$67.35 
59.32 

$51.27 
27.75 

$983.27 
742.19 

$32148.91 
14269.90 

9 

$90.00 
37.17 

$86.95 
14.75 

$836.92 
775.48 

$33197.84 
19057.55 

152 


FOURTH   YEAE 


[Written 


DRILL   WORK 


Multiply  and  test : 


1.   8465 

a  22 

2.   7645 

6  45 

3.   8741 

c50 

Form  100  problems  by  mul- 

4.  9860 

d86 

tiplying  each  multiplicand  by 

5.  8425 

6.  9654 

by 

e76 
/98 

each  multiplier, 
la   22x8465  = 

as: 

7.   7869 

5-66 

Id  86x8465  = 

=  ? 

8.   9765 

h  69 

6  e   76  X  9654  = 

=  ? 

9.  4875 

t97 

10.    8420 

i89 

11.   Divide  969  by  23. 

12.  Divide  969  by  24. 

42* 

40^ 

23)969 

24)969 

92 

96 

49 

9 

46      Test.  — 42  x 

23  =  966 

3                   966 

+  3  =  969 

Divide  and  test : 

13.    84765 

1 

a  86 

14.    57672 

&78 

Form    64 

problems    by 

15.    80720 

c91 

dividing  eacL 

I  of   the  divi- 

16.  50724 

17.  60925 

•by 

^59 

'e72 

dends  by  each  of  the  divi- 
sors, thus : 

18.    86412 

/67 

13  a  84765^ 

-86=? 

19.    76412 

^82 

13  c  84765^ 

-91  =  ? 

20.    83456 

/i65 

18  e   86412 ^ 

-72=? 

Written] 


FRACTIONS 


153 


I 


ADDITION   AND   SUBTRACTION   OF   HALVES 
AND   FOURTHS 

Halves  Fourths 

I  equal  one  whole  unit ; 


h+i 


or  1. 


f  equal  one  whole  unit; 

+i  +  i  +  i  =  |  or  1. 


/2 


=  \y4 


=     1 

4 


+     1 

^         4 


4  ' 


l4-l=-l-    1+14-1  =  1 
2^4        4'2~4~4        4' 


^■2        4        4'4        2        4'4 

First  add,  then  subtract : 

3.    51  4.    9|  5. 

3^  8J        ■ 


V4 


6.    51 


7.     8f 

2J 


Add: 
8.    31 


iH 


671 


10. 


651 


11. 


25| 
9i 


12. 


561 
8i 


Tn  example  8,  |+}  =  |  or  1 ;   1  +  1  =  11      Write  the 
fraction  J  and  add  the  1  to  the  whole  number. 


154 


FOURTH   YEAR 


[Written 


HALVES,   FOURTHS,   AND   EIGHTHS 

Halves  Fourths  Eighths 


1-    i  =  t  =  t-  f  +  l  +  i  =  t-     _         s 

2.  Compare  ^  and  J  of  the  same  circle. 

3.  Compare  ^  and  ^  of  the  same  circle. 

4.  J  is  what  part  of  ^  ?     f  =  ^  =  i- 

e     1— i..  1  — -L-  1.4.1  4.1  — r-  i_i_i. 

^-     2~'8J4:~~8'2^8^4:"~8?2        8~"8* 

6.   Into  how  many  eighths  can  the  whole  circle  be 
divided?   into  how  many  fourths? 
Add: 


7.   3J 

H 

ii 

8.    7f 

9.   61 
9| 

10. 

9i 
11 

6^ 

11.   5J 

121 
31 

12-   |  +  f  +  f  =  f,  or 
many  whole  units  ? 
Subtract,  then  add : 

2  whole  units; 

t+l 

+  f  =  how 

13.     lOf 

5i 

14.    121 
6i 

15.    27f 

«8 

16. 

191 
6i 

17.   361 

16| 

18.   62f 

31| 

19.   63| 
39^ 

20.   26| 

24| 

21. 

18| 

22.    40| 

20i 

Written] 


FRACTIONS 


155 


THIRDS,    SIXTHS    AND   NINTHS 

Thirds  Sixths  Ninths 


i 

1 

= 

f 

1-  i+f  =  |; 

2-  i+l  +  i  = 

4  or— unit;   J  + 

9=?;  2  = 

i+i=f 

First  add  and  then  subtract : 

3.    15| 
10| 

4.  29^ 
13^ 

5.     81| 

20* 

6.  42| 
13i 

7.   62f 
12i 

8.    15f 
12| 

9.     16J 

lOi 

10.   19| 

12i 

11.  Mrs.  Clark  bought  If  dozen  lemons  and  used  IJ 
dozen.     How  many  remained  ? 

12.  Henry  studies  41  hours  a  day,  and  James  6J 
hours.  How  much  longer  does  James  study  each  day 
than  Henry? 

13.  A  flower  bed  is  4i  ft.  long  and  2|  ft.  wide.  Find 
the  distance  aground  it. 

14.  If  it  takes  Henry  3J  hours  to  walk  a  certain  dis- 
tance, or  11  hours  to  ride  it  on  his  bicycle,  how  much 
time  does  he  save  by  riding  ? 


156                                FOURTH 

YEAR 

MULTIPLICATION 

1.   Multiply  794  by 

326. 

694 

694 

326 

326 

4164=     6x694 

4164 

13880=   20x694 

1388 

208200  =  300x694 

2082 

[Written 


226244  =  326  x  694  226244 

When  multiplying  by  3  hundreds,  write  the  partial 
product  as  2082  hundreds  by  placing  the  first  figure  of 
that  product  under  hundreds. 

Multiply : 
2.   462  3.   283  4.   619  5.    543 

375  *      243  128  264 

6.    $40.75        7.    $26.73        8.   $38.27        9.   $46.75 
325  364  918  842 


10.  465  by  327     17.    5382  by  147  24.  $46.75  by  275 

11.  289  by  943     is.   2493  by  316  25.  $83.94  by  843 

12.  568  by  769     19.   9875  by  827  26.  $76.15  by  972 

13.  987  by  938     20.   7341  by  695  27.  $39.85  by  867 

14.  478  by  783     21.   9386  by  783  28.  $48.57  by  984 

15.  925  by  867     22.   6294  by  894  29.  $  96.78  by  786 

16.  387  by  591     23.    9387  by  619  30.  $39.74  by  815 
31.   Announce  products  at  sight : 

20x40               50x50               12x12  80x80 


Written]  MULTIPLICATION 

MULTIPLICATION 
1.   Multiply  273  by  304. 

273 
304 


157 


1092 
000 
819 

82992 


273 

304 
1092 

819 

82992 


Do  not  multiply  by  0  as  in  the  first  illustration. 

When   multiplying   by  3  hundreds,  write  the   partial 

product   as    819  hundreds  by  placing  the  right  hand 
figure  of  that  product  in  hundreds'  place. 


2. 

3. 

4. 

402 

$30.60 

■  $20.75 

x503 

X2040 

xl05 

1206 

122400 

10375 

2010 

6120 

2075 

202206 

$62424.00 

$2178.75 

5.  316 

6.  275 

7.  428 

8.  506 

x502 

x306 

x405 

x30V 

9.  243 

10.  709 

11.  608 

12.  705 

x308 

x504 

x209 

x804 

ks.  $8.08 

14.  $40.75    15. 

$90.70 

16.  $38.04 

1   x607 

x603 

x504 

x703 

158 

FOURTH  YEAR 

[Written 

How  many  are 

1. 

704x3096 

6. 

309  X  4039 

11. 

803  X  $40.70 

2. 

809  X  9409 

7. 

907  X  7008 

12. 

709x$75.2£ 

3. 

609  X  7320 

8. 

408  X  6007 

13. 

304  x$  68.07 

4. 

507  X  8060 

9. 

502x9103 

14. 

508  x$  70.95 

5. 

608  X  3724 

10. 

903  X  7030 

15. 

806  x$  48.57 

Multiply : 

16. 

8945  by  643 

26. 

6785  by  904 

36. 

5078  by  206 

17. 

3089  by  136 

27. 

7856  by  685 

37. 

9067  by  508 

18. 

4506  by  275 

28. 

9786  by  607 

38. 

8906  by  379 

19. 

3875  by  609 

29. 

7869  by  783 

39. 

6709  by  806 

20. 

5783  by  382 

30. 

6778  by  579 

40. 

6076  by  927 

21. 

3296  by  907 

31. 

9868  by  632 

41. 

8405  by  403 

22. 

7395  by  834 

32. 

5846  by  597 

42. 

6035  by  876 

23. 

3837  by  958 

33. 

6484  by  460 

43. 

8708  by  804 

24. 

6574  by  687 

34. 

9676  by  329 

44. 

7083  by  705 

25. 

8936  by  706 

35. 

6798  by  376 

45. 

5067  by  770 

46.  Mr.  Watson  had  2475  boxes  of  soap.  Each  con- 
tained 175  cakes.     Find  the  entire  number  of  cakes. 

47.  A  factory  averages  2485  articles  for  310  days  of 
the  year.     What  is  the  entire  number  made  ? 

48.  Mrs.  Thompson  raised  246  turkeys  and  sold  them 
at  $  1.75  each.     How  much  did  she  receive  for  them? 

49.  A  suit  factory  manufactured  3685  suits  during  the 
season.  At  $  28.50  each,  how  much  was  received  for 
them? 


Oral  and  Written]      MULTIPLICATION  159 

PARTS   OF   NUMBERS 

1.    Find  I  of  24. 

^     f  94.  •     Q  .  How  do  we  find  ^  of  a  mim- 

I  of '24 = 2  xl  ov  16.  ^''  ^  i  °f  ^  j'T)''  •  *  t ' 

•^  number,  etc.  ?   |  ot  a  number 

of  the  number.    #  of  a  number  =  3  x  ^  of  the 


'AX 


number,  etc. 

Give  rapidly. 

2.  i  of  each  number:  16,  24,  36,  44,  48,  50. 

3.  J  and  I  of  each  number  :  15,  18,  24,  36,  45. 


4. 

i  and  f  of  each  number :  16,  20,  28,  3 

2,  48. 

5. 

h  h  h  ^^d  1 

of  each  number :  20,  35, 

45,  40,  80. . 

Find: 

6. 

iofl8 

12. 

foflS 

18.   fof21 

24.    |of75 

7. 

lof24 

13. 

f  of  28 

19.   fof20 

25.   |-of75 

8. 

lofl6 

14. 

|of  56 

20.    f  of  40 

26.   |of96 

9. 

lof  42 

15. 

iof  64 

21.   J  of  24 

27.   i  of  144 

10. 

fof24 

16. 

lof  63 

22.    f  of  65 

28.   f  of  160 

11. 

fof  25 
Find: 

17. 

|of  63 

23.    |of48 

29.  1  of  255 

30. 

1  of  $24 

35.  f  1 

3f  12  lb.               40. 

^  of  $8.20 

31. 

|of  $16 

36.    f  ( 

Df  9  ft.                  41. 

^of  $12.60 

32. 

1  of  $50 

37.    1. 

Df  12  yd.          42. 

1  of  $20.40 

33. 

f  of  $18 

38.    f  1 

oi  16  gal.         43. 

1  of  $15.90' 

1  of  $20 

39.    f  of  8  bu.                 44. 

1  of  $24.20' 

160  FOURTH  YEAR  [Written 

MULTIPLICATION   BY   MIXED   NUMBERS 
1.   Multiply  36  by  6f. 
36 

2. 

means  that  f  of  36  is  to 


21^ 

;  =  6  x36  be  added  1 

24C 

)  =  6f 

x36 

Multiply 

2. 

72 

by8| 

3. 

126 

by9f 

4. 

324 

byl2J 

5. 

872 

by25f 

6. 

966 

by  124| 

7. 

848 

by  238f 

8. 

489 

by  372^ 

9. 

1248 

by  309f 

10. 

2530 

by  842f 

11. 

3575 

by  909f 

12. 

8496 

by  890f 

13. 

3660 

by  780J 

14. 

8575 

by  197J 

15. 

8496 

by  875f 

16. 

9639 

by  976f 

17. 

8472 

by  865i 

18. 

8436 

by  345i 

19. 

9764  by  876| 

20. 

9972  by  984| 

21. 

8848  by  787f 

22. 

7266  by  719f 

23. 

8755  by  394f 

24. 

9875  by  485f 

25. 

9672  by  872§ 

26. 

6488  by  797| 

27. 

7465  by  864f 

28. 

7280  by  6201 

29. 

4860  by  701f 

30. 

5050  by  500| 

31. 

6006  by  303| 

32. 

9608  by  490f 

33. 

8570  by  809f 

34. 

6099  by  789f 

35. 

7085  by  804| 

Oral]  PARTS   OF  A  DOLLAR  161 

FRACTIONAL    PARTS   OF   A   DOLLAR 


$.50=  ^of  $1.00 

$.12|=  iof  $1.00 

$.25=  |of  $1.00 

$.06i=Xof  $1.00 

$.20=  Iof  $1.00 

$.33|=|of  $100 

$.10  =  ^of  $1.00 

$.16|=  |of  $1.00 

$.40=  |of  $1.00 

$.75    =  |of  $1.00 

Give  at  sight  the  cost  of : 

1.  6  bushels  of  apples  at  $  .50  a  bushel. 
Hint.  — 6x^1  =  ^1  =  ^3. 

2.  8  gallons  of  vinegar  at  $  .25  a  gallon, 

3.  8  yards  of  silk  at  $  .50  a  yard. 

4.  8  pounds  of  meat  at  $  .121  a  pound. 

5.  10  dozen  eggs  at  $  .20  a  dozen. 

6.  9  yards  of  muslin  at  $  .10  a  yard. 

7.  6  pecks  of  pears  at  $.25  a  peck. 

8.  12  pictures  at  $  .75  each. 

9.  10  yards  of  lawn  at  $  .10  a  yard. 

10.  6  gallons  of  vinegar  at  $  .50  a  gallon. 

11.  8  gallons  of  oil  at  $  .25  a  gallon. 

12.  12  dozen  oranges  at  $  .25  a  dozen. 

13.  6  bushels  of  apples  at  $  .50  a  bushel. 

14.  16  pounds  of  rice  at  $  .121  a  pound. 

15.  10  pecks  of  peaches  at  $  .20  a  peck. 

16.  8  gallons  of  milk  at  $  .12|^  a  gallon. 


16 

2 

FOUETH 

YEAR 

[Oral  and  Written 

DIVISION 

Give  quotients  at  sight : 

1. 

a 
100^ 

10   280- 

h140 

c 

993^ 

331    315  + 

105 

2. 

500^ 

50   930- 

^310 

645^ 

129    972-+ 

324 

3. 

300^ 

30   860- 

-172 

951h- 

317    725  + 

145 

4. 

250^ 

50   396- 

i-132 

284H- 

142    932  H- 

466 

5. 

400-^ 

80,  960- 

h320 

788  H- 

197    260  + 

130 

€. 

844-^211   990- 

-330 

882^ 

126    775  + 

155 

7. 

Divide 

175608  by 

324. 

8.  Divide  793320  by 

264. 

542 
324)175608 
1620 
1360 
1296 

3005 

264)793320 

792 

1320 

1320 

648 

648  , 
do 

Since  264  is  lar 
we  write  in  the 

ger  than  13,  what 
quotient  ? 

Divide 

9 

63596 

a 

by  126 

46785 

6 
by  135 

c 
13940  by 

340 

10 

78563 

by  341 

78568 

by  244 

81282  by 

408 

11 

.  48842 

by  144 

65375 

by  255 

23674  by 

726 

12 

.  26786 

by  354 

78634 

by  184 

83765  by 

415 

13 

.  46785 

by  165 

79673 

by  263 

27854  by 

129 

14 

.  83761 

by  219 

86572 

by  196 

76348  by 

366 

Written]  PRACTICAL  PROBLEMS  163 

PROBLEMS   OF   TWO   OPERATIONS 

1.  A  dairyman  has  137  cows  in  one  herd  and  47  less 
in  another.     How  many  cows  has  he  ? 

Study  of  Problem 
137  No.  cows  in  one  herd.  1.   What  is  given  in  this 

47  No.  less  in  2d  herd.  problem  ? 

~90  No.  cows  in  2d  herd.  «•    The    number    of 

cows  in  one  herd. 
137  cows +  90  COWS  =227  cows.  h.   The  difeerence  in 

the  number  in  the  two 
herds. 

2.  What  is  required  in  the  problem  ? 
a.   The  number  in  the  second  herd. 
h.    The  number  in  both  herds. 

3.  How  can  you  find  what  is  required  from  what  is  given  ? 

a.   By  subtracting  the  difference  from  the  number  in  the 

first  herd. 
6.    By  adding  the  number  of  cows  in  the  two  herds. 

Note.  —  The  purpose  of  these  studies  is  threefold : 

1.  To  train  the  pupil  to  see  and  understand  the  conditions  of 
the  problem. 

2.  To  give  a  logical  grasp  of  the  conditions  of  the  problem.  . 

3.  To  direct  the  teacher  in  his  efforts  to  attain  these  ends. 

2.  A  man  has  267  sheep  in  one  field  and  88  less  in 
another.     How  many  sheep  has  lie  ? 

3.  A  merchant  has  $496  in  the  safe  and  $175.25 
less  in  the  bank.  How  much  money  has  he  in  both 
places  ? 

4.  A  man  sold  a  farm  for  $7625  and  gained  $1685. 
How  much  would  he  have  received  for  it  if  the  gain 
had  been  $2675? 


164  FOURTH  YEAR  [Written 

5.  A  man's  salary  is  $950  per  year.  He  pays  $260 
for  board,  $136  for  clothing,  and  $115.75  for  other 
expenses.     How  much  has  he  left  ? 

6.  A  grocer  deposited  in  bank  dm-ing  the  week  the 
following  sums :  $495.65,  $283.75,  $693.29,  $75.80, 
$249.89,  and  $375.77.  After  making  the  last  deposit, 
lie  found  there  was  a  balance  to  his  credit  of  $1265.15. 
How  much  had  he  withdrawn  ? 

7.  If  a  freight  car  costs  $475,  and  a  locomotive 
$14625,  what  is  the  value  of  a  train  containing  27  cars 
and  a  locomotive  ? 

8.  A  woman  sold  at  a  store  16  doz.  eggs  at  18^  a 
dozen,  13J  lb.  of  butter  at  28^  a  pound,  and  27  lb.  of 
dressed  chicken  at  16^  a  pound.  How  much  did  she 
receive  for  all  ? 

9.  A  lady  bought  at  a  store : 

8  lb.  of  coffee®  28^; 
9^1b.  of  rice®  8^; 

24  lb.  of  sugar  ®  5^; 

8  cans  tomatoes  ®  13^; 
20  cans  beans  @  19  ^. 

Find  the  amount  of  her  purchases. 

10.  Find  the  cost  of : 

271  lb.  of  cheese  ®  18^; 
14|  lb.  of  lard  ®  12^; 
17  Ib.of  butter  ®  27^; 

25  bottles  ammonia  ®  8  ^ ; 
12  cans  peas  ®  18  ^. 


$  2.75 

3.65 

4.75 

6.75 

1.75 

12.75 

6)§32.40 

in  6  days. 

$5.40  ; 

average  each 

day. 

Written]     PEOBLEMS   OF  TWO   OPERATIONS  165 

11.  A  man  earned  each  day  in  one  week  as  follows : 
$2.75,  $3.65,  $4.75,  $6.75,  $1.75,  $12.75.  Find  his 
average  daily  earnings. 

Study  of  Problem 

1.  What  is  given  in  this 
problem  ? 

2.  What  is  required  ? 

3.  What  is  the  first  step 
in  the  solution  ?    the  second  ? 

4.  Why  do  you  divide  by 
6  to  find  the  average  ? 

5.  Show  that  the  answer 
is  correct. 

12.  Two  men  contribute  equal  amounts  to  buy  a  lot  for 
£875;  to  build  a  storeroom  for  $4860;  for  furniture, 
$520;  and  for  goods  to  begin  business,  $5785.  How 
much  does  each  pay  ? 

13.  A  creamery  received  milk  for  six  days  as  follows  : 
7640  gallons,  8675  gallons,  9634  gallons,  8432  gallons, 
8763  gallons,  and  8604  gallons.  What  were  the 
average  daily   receipts? 

14.  If  Helen  received  85  in  arithmetic,  79  in  gram- 
mar, 89  in  history,  92  in  geography,  86  in  physi- 
ology, and  85  in  writing,  what  was  her  average  in  these 
studies  ? 

15.  The  attendance  at  a  school  was  604  on  Monday, 
607  on  Tuesday,  598  on  Wednesday,  603  on  Thursday, 
598  on  Friday.  What  was  the  average  daily  attend- 
ance for  the  week  ? 


166  FOUKTH  YEAR  [Written 

16.  39  ladies'  suits,  each  requiring  12  yards,  were  made 
from  a  lot  of  cloth  containing  576  yards.  How  many 
yards  were  left  ? 

Study  of  Problem 

12  yd.  in  1  suit. 

on  1.    State  this   problem  in 
0\j  number  of  suits.  ,, 
another  way. 

J-^^  2.    What  operation  is  em- 

36  ployed  in  the  first  step  in  the 

468  yd.  in  39  suits.  solution  ?  in  the  second  ? 

3.   Prove  that  the  answer 

576  yd.  -  468  yd.  =  108  yd.      i,  eorrect. 

17.  A  boy  sold  16  books  at  20  cents  each,  and  36  toys 
at  26  cents  each.  How  much  more  did  he  receive  for 
the  toys  than  for  the  books  ? 

18.  Mr.  Boyd's  mail  route  is  23J^  miles,  and  Mr.  Bur- 
ton's is  17|^  miles.  How  much  farther  does  Mr.  Boyd 
travel  in  84  days  than  Mr.  Burton  ? 

19.  A  school  term  is  180  days.  If  James  attends  ^ 
of  the  term,  how  many  days  is  he  absent  from  school  ? 

20.  A  bookkeeper  receives  $150  a  month,  and  saves 
$68  a  month.     How  much  does  he  spend  in  a  year? 

21.  Harry  works  48|^  hours  after  school  each  month, 
at  12  cents  per  hour,  and  Henry  52|  hours  at  16  cents 
per  hour.     Find  the  difference  in  their  wages. 

22.  What  is  the  difference  between  the  cost  of  17 
horses  at  $156  each,  and  69  cows  at  137  each? 

23.  A  merchant  buys  28  bbl.  of  sugar  at  $23  a  barrel, 
and  36  bbl.  at  $24  a  barrel.  If  he  sells  all  for  $1856, 
how  much  does  he  gain  ? 


Written]     PROBLEMS   OF  TWO  OPERATIONS  167 

24.  A  merchant  paid  $420.48  for  carpet,  and  sold  it 
for  $569.40.  If  he  gained  17^  on  each  yard,  how- 
many  yards  did  he  buy  ? 

Study  of  Problem 

$569.40  selling  price  of  all.  1.    What   do   you  mean 


"  9 


420.48  cost  price  of  all.  ^j  the  terra  "  cost 

$~~TJq~(vo  r^^ir.  r.(  r^^  2.    What  (lo   vou   mean 

148.9  J  gam  of  all.  •      „o    u 

by    "  selling    price "  f    by 


Gain  on 


"  gain  "  ? 


3.   How  do  you  find  the 
1yd.    $. 17)  S  148.92  gain  on  all.  total  gain  ? 

876  times,  or  yd.  4.   Prove    that   the    an- 

swer is  correct. 

25.  I  bought  land  for  $1850,  and  sold  it  for  $2294, 
thereby  gaining  $6  an  acre.  How  many  acres  did  I 
buy? 

26.  A  drover  bought  cows  for  $1500,  and  sold  them 
for  $2250.  If  he  gained  $15  on  each,  how  many  did 
he  buy  ? 

27.  Mr.  Kinney  paid  $2640  for  a  city  lot,  and  sold  it 
for  $4560.  If  he  gained  $24  a  front  foot,  how  many 
front  feet  did  he  sell  ? 

28.  The  population  of  a  town  was  8675  in  1900, 
and  12635  by  a  special  census  taken  in  1905.  What 
was  the  average  yearly  increase  ? 

29.  Mr.  Beggs  paid  $288  rent  last  year.  This  year 
he  pays  $36  less.     What  is  his  rent  per  month  ? 

30.  A  jeweler  bought  rings  for  $140  and  sold  them 
for  $160.  If  he  gained  $.50  on  each,  how  many  did  he 
buy? 


$1.60  daily  wages. 

16  number  of  days  worked. 

9  60 

16  0 

$25.60  total  wages. 

Price  of               40  times,  or  bushels, 

168  FOURTH  YEAR  [Written 

31.  A  laborer  worked  16  days  at  $1.60  a  day,  and 
with  his  earnings  bought  potatoes  at  64)2^  a  bushel. 
How  many  bushels  did  he  receive  ? 

Study  of  Problem 

1.  State  this  problem 
in  another  way. 

2.  How  can  we  find 
the  total  amount  earned? 

3.  What  operation  io 
involved  in  the  first  step 
of  the  solution  ?  in  the 
second  step  ? 

1  bu.  $.64)$25.60  total  wages.  4.   Prove  that  the  an- 

swer is  correct. 

32.  If  124  bags  of  coffee,  each  weighing  48  lb.,  were 
bought  for  $729.12,  what  was  the  price  per  pound  ? 

33.  At  20  i^  per  hour  how  long  will  it  take  a  laborer 
to  earn  $80,  working  8  hours  per  day? 

34.  If  96  bu.  of  corn  sell  for  $60.48,  what  is  the 
value  of  250  bushels  at  the  same  price  ? 

35.  A  trackman  averages  2  miles  per  hour  for  8 
hours  each  day.  His  record  book  shows  960  miles 
walked.     Find  the  number  of  days. 

36.  If  a  dozen  lemons  cost  $.36,  how  much  will  840 
lemons  cost  ? 

37.  If  25  bbl.  of  flour  weigh  4900  lb.,  how  much  will 
56  bbl.  weigh  ? 

38.  If  23  carriages  cost  $4025,  how  much  are  84 
such  carriages  worth  ? 


Written]      PKOBLEMS  OF  TWO  OPERATIONS  169 

39.  If  600  bu.  of  shelled  corn  weigh  33,600  lb.,  how 
much  will  468  bu.  weigh  ? 

40.  When  9  bales  of  cotton,  weighing  325  lb.  each, 
sell  for  $  731.25,  what  is  the  price  per  pound  ? 

41.  If  a  peach  basket  holds  2  pecks,  how  many- 
bushels  are  there  in  12. carloads,  each  containing  456 
baskets  ? 

42.  How  many  books  each  2  inches  thick  can  be 
placed  in  a  bookcase  containing  4  shelves,  each  shelf 
of  which  is  3  ft.  in  length  ? 

43.  If  123  tons  of  coal  cost  $725.70,  how  much  will 
16  tons  cost  ? 

44.  24  cords  of  wood  cost  $90;  how  much  will  18 
cords  cost  at  the  same  rate  ? 

45.  If  a  newsboy  earns  $19.98  in  18  days,  how  much 
will  he  earn  at  the  same  rate  in  360  days  ? 

46.  When  525  gallons  of  milk  sell  for  $84,  for  how 
much  will  715  sell  ? 

47.  Mary  bought  16  pounds  of  coffee  at  14^  a  pound, 
8  lb.  of  butter  at  28^  a  pound,  and  12  cans  of  corn  at 
15^  a  can.  She  gave  the  merchant  in  payment  a  $10 
bill.     How  much  change  should  she  receive  ? 

48.  A  drover  sold  56  sheep  at  $4  each,  8  cows  at 
$36  each,  and  48  hogs  at  $12  each.  If  he  received 
$275  on  the  day  of  the  sale,  how  much  is  still  due  him  ? 

49.  A  lady  had  $100.  If  she  bought  4  chairs  at  $6 
each,  a  couch  for  $28,  and  a  rocking  chair  for  $16, 
how  much  had  she  left? 


170  FOURTH  YEAR  [Written 

50.  I  bought  57  yards  of  cloth  at  25)^  a  yard,  and  16 
yards  of  matting  at  2%P  a  yard.     Find  the  cost  of  both. 

51.  A  lady  sold  6  doz.  eggs  at  18  cents  a  dozen,  and 
8  lb.  of  butter  at  27  cents  a  pound.  How  much  did  she 
receive  for  both  ? 

52.  A  merchant  bought  546. bbl.  of  pork  at  $  16.25  a 
barrel,  and  sold  it  so  as  to  gain  $1638.  At  what 
price  per  barrel  did  he  sell  the  pork  ? 

53.  James  earned  $  1.50  per  day  and  saved  85  cents. 
If  his  savings  were  $  33.15,  how  many  days  did  he  work  ? 

54.  A  farmer  bought  4  horses  at  $  137  each,  7  cow^s 
at  $27  each,  and  38  sheep  at  $6.50  each.  Find  tlie 
cost  of  all. 

55.  What  will  be  the  cost  of  108  lb.  of  ham  at  16i 
cents  a  pound,  and  48  lb.  of  breakfast  bacon  at  18  cents 
a  pound  ? 

56.  Two  automobile  parties  travel  in  opposite  direc- 
tions, one  at  an  average  of  127  miles,  the  other  at  78 
miles  a  day.     How  far  apart  will  they  be  in  16  days  ? 

57.  A  factory  employs  56  men  at  $  1.75  a  day,  and 
12  men  at  $  2.25  a  day.  Other  expenses  are  $  125  a  day. 
How  much  does  it  cost  to  run  the  factory  26  days  ? 

58.  A  man  paid  $  165  for  a  carriage,  and  3|  times  as 
much  for  a  span  of  horses.  How^  much  did  he  pay  for 
both? 

59.  Mr.  Hall  deposited  in  the  bank  $  24  a  month 
for  8  months,  and  $  27  a  month  for  4  months.  How 
much  did  he  deposit  in  the  year  ? 


ritten] 

DIVISION 

REVIEW   OF 

DIVISION 

Divide  and  test : 

1. 

84563  by  224 

13. 

95846  by  675 

2. 

45675  by  125 

14. 

37846  by  332 

3. 

46752  by  236 

15. 

92846  by  124 

4. 

84252  by  342 

16. 

45983  by  475 

5. 

78654  by  375 

17. 

32841  by  243 

6. 

98740  by  425 

18. 

92384  by  752 

7. 

97601  by  438 

19. 

66008  by  300 

8. 

98700  by  508 

20. 

15899  by  122 

9. 

80070  by  710 

21. 

77443  by  224 

10. 

81704  by  508 

22. 

59823  by  525 

11. 

99999  by  999 

23. 

78912  by  640 

12. 

50321  by  637 

24. 

93408  by  825 

Find 

quotients  and  test : 

25. 

136425^405 

35. 

604325 -^  304 

26. 

246840 -^  476 

36. 

708546-^222 

27. 

332468^332 

37. 

125745^125 

28. 

948562-^450 

38. 

985432^112 

29. 

476352^221 

39. 

756342^102 

3b. 

789324 -^  552 

40. 

354725^256 

31. 

569239 -f- 334 

41. 

498075^401 

32. 

159909^115 

42. 

987260 -^- 200 

33. 

550550-^155 

43. 

800745-^310 

34. 

889034-^324 

44. 

584972 -^  226 

171 


172  FOURTH  YEAR        [Oral  and  Written 

COMBINING   PROCESSES 

1.  6  +  4  +  8-7  +  4-9  =  ? 

2.  7  +  6-5-4  +  9-6  =  ? 

The  parenthesis  (  )  indicates  that  all  numbers  in- 
closed by  it  are  to  be  considered  as  one  number ;  thus, 
(7  +  9)  -  (4  +  5)  means  that  the  sum  of  4  and  5  is  to  be 
taken  from  the  sum  of  7  and  9. 

The  vinculum  ( )  is  sometimes  used  instead  of 

the  parenthesis ;  thus,  7  +  9  —  4  +  5  =  7. 

Solve : 

3.  9  +  8- (6 +  6) +  7-3  =  ? 

4.  8  +  6  +  16-7-8  +  6  =  ? 

5.  26 +  38 -(48 -23) +  16  =  ? 

6.  87-42  +  96-72  +  26  =  ? 

7.  (97 -35) -26 +  14 +  78  =  ? 


8.   86-48  +  56-28-47  =  ? 

COUNTING   BY   MIXED   NUMBERS 

1.   Count  by  2^  to  40  ;  by  3^  to  40  ;  by  61  to  50. 


2.   Announ 

ce  at  sight : 

11x4 

Ux  6 

11x6 

lix4 

2Jx4 

21  X  6 

21x6 

21x4 

31x4 

3Jx6 

31x6 

31x4 

4ix  4 

4|x6 

41x6 

4|  x4 

o. 


Build  similar  tables  with  1-|,  1^,  and  1|-. 


Oral]  ANALYSIS  173 

ANALYSIS 

1.  Find  the  cost  of  3  doz.  oranges  at  20  ^  per  dozen. 
1  doz.  oranges  cost  20 ^;  3  doz.  cost  3  times  20 ^  =  60  ^. 

2.  At  12  cents  a  quart  for  berries,  how  much  will 
8  quarts  cost  ? 

3.  At  30  ^  a  peck,  how  much  will  a  bushel  of  beans 
cost? 

4.  When  peaches  are  50  cents  a  basket,  how  much 
will  7  baskets  cost  ? 

5.  A  ton  of  coal  costs  $5.     How  much  will  9  tons 
cost? 

6.  A  boy  rides  his  w^heel  6  miles  in  one  hour.     How 
far  will  he  ride  in  7  hours  ? 

7.  When  5  boxes  of  matches  cost  50^,  how  much 
will  1  box  cost  ? 

Cost  of  5  boxes  =  50  ^ ; 

Cost  of  1  box     =  i  of  50^,  or  10^. 

8.  A  boy  bought  4  balls  for  80  cents.     How  much 
was  that  apiece  ? 

9.  When  8  yards  of  velvet  cost  $24,  how  much  will 
1  yard  cost  ? 

10.  A  box  of  shoes  containing  12  pairs  costs   $36. 
Find  the  cost  per  pair. 

11.  Six  cows  were  sold  for  $246.      What  was  the 
average  selling  price  ? 

12.  When  a  telegram  of  10  words  costs  40  cents, 
what  is  the  average  cost  of  each  word  ? 


174  FOURTH   YEAR  [Oral 

ANALYSIS 

1.  When  1  pencil  costs  10  ^,  how  many  can  you  buy 

for  60  ^  ? 

When  1  pencil  costs  10  ^,  for  60  ^  you  can  buy  as  many  pen- 
cils as  10  ^  is  contained  in  60  ^. 

2.  At  12  ^  per  yard,  how  many  yards  of  ribbon  can 
be  bought  for  96^? 

3.  Cherries  are  8  ^  a  quart.     How  many  quarts  can 
be  bought  for  72  ^  ? 

4.  When  3  tons  of  coal  cost  $18,  how  much  will  7 

tons  cost  ?  Cost  of  3  tons  =  118; 

Cost  of  1  ton  =  1  of  $  18,  or  $6; 
Cost  of  7  tons  =  7  X  $6,  or  $42. 

5.  How   much   will    9   dozen  lemons  cost  when  3 
dozen  sell  for  45  cents  ? 

6.  Three  men  earn   $30  in  a  certain  time.     How 
much  will  8  men  earn  in  the  same  time  ? 

7.  When  1  a  bushel  of  potatoes  sells  for  25  cents, 

how  much  will  3  bushels  cost  ? 

Cost  of  ibu.=  25^; 

Cost  of  i  bu.  =  2  X  25^,  or  50^; 

Cost  of  3  bu.  =3  X  50^,  or  $1.50. 

8.  At  20  cents  a  peck,  how  much  will  2  bushels  of 
apples  cost  ? 

9.  When  milk  is  selling  at  5  ^  a  quart,  how  much  will 
3  gallons  cost  ? 

10.    If  J  of  a  yard  of  velvet  costs  60  ^,  how  much  will 
2  yards  cost  ? 


Oral  and  Written]  COMPARISON  175 

COMPARISON 

1.  Compare  80  and  20 ;  60  and  30 ;  90  and  10. 

2.  2-1  is  what  part  of  5  ?  of  10  ?  of  15  ?  of  20  ? 

3.  31  is  what  part  of  10  ?  of  20?  of  30?  of  6f  ? 

4.  Compare  3-%  and  ^^ ;  y%  and  ^  ;  ^-g  and  y^^. 

5.  What  part  of  25  is  5  ?  is  6^  ?  is  21  ?  is  8I  ? 

6.  What  part  of  6  pk.  is  2  pk.?  of  10  gal.  is  2  gal.? 

7.  3  pk.  is  what  part  of  1^  bn.  ?  of  21  bu.  ? 

8.  8  oz.  of  butter  is  what  part  of  2  lb.  ?  of  21  lb.  ? 

9.  When   21  pounds  of  butter  cost  90  cents,  how 
much  will  9  pounds  cost  ? 

9  pounds  equal  4  x  2 J  pounds ;  hence,  9  pounds  will  cost  4  x  90 
cents,  or  $3.60. 

10.  If  J  a  ton  of  hay  costs  $7.50,  how  much  will  4 
tons  cost  ? 

11.  When  2  pecks  of  potatoes  cost  50  cents,  how 
much  will  1^  bushels  cost  ? 

12.  When  butter  is  selling  at  3  pounds  for  $|,  how 
much  will  15  pounds  cost  ?  • 

13.  When  2^  dozen  buttons  sell  for  30  cents,  how 
much  will  7J  dozen  cost  ? 

14.  If  61  tons  of  coal  cost  $37.50,  how  much  will 
25  tons  cost  ? 

15.  If  7^  yards  of  velvet  cost  $11.40,  how  much  will 
15  yards  cost  ?  How  many  yards  can  be  bought  for 
$22.80? 


176  FOURTH  YEAR  [Written 

16.  A  boy  picked  18  quarts  of  chestnuts  and  sold 
them  at  the  rate  of  2  quarts  for  25  cents.  How  much 
did  he  receive  for  them  ? 

17.  If  3  pounds  of  steak  cost  48  cents,  how  much 
will  10  pounds  cost  ? 

18.  A  farmer  raised  40  bushels  of  shelled  corn  per 
acre  on  7^  acres.  At  the  same  rate,  how  many  bushels 
«^^ould  he  raise  from  22|  acres  ? 

Find  the  cost  of : 

19.  288  chairs,  when  9  chairs  cost  $6.75. 

20.  350  rings,  when  7  rings  cost  $  19.74. 

21.  285  fans,  when  5  fans  cost  $  1.75. 

22.  144  knives,  when  6  knives  cost  $  5.04. 

23.  78  vases,  when  6  vases  cost  $  17.76. 

24.  248  hats,  when  8  hats  cost  $  15.68. 

25.  24  pictures,  when  4  pictures  cost  $  18.92. 

26.  48  lamps,  when  16  lamps  cost  $34.56. 

27.  54  clocks,  when  27  clocks  cost  $  72.63. 

28.  28  desks,  when  14  desks  cost  $  173.32. 

29.  78  rockers,  when  26  rockers  cost  $  196.30. 

30.  36  watches,  when  18  watches  cost  $702. 

31.  36  cords  of  wood,  when  6  cords  cost  $  35.04. 

32.  128  tons  of  coal,  when  8  tons  cost  $57.60. 

33.  180  quarts  of  milk,  when  18  quarts  cost  $  1.08. 

34.  56  crates  of  melons,  when  8  crates  cost  $  28.80. 

35.  328  books,  when  8  books  cost  $  1.44. 


Written] 


BILLS 
BILLS 


17V 


Pittsburg,  Pa.,  ^ee.  /,  1907. 

Mu  L.  m.  ^ka^yu^, 

67  S^&oaI  ^t. 

aSotigfjt  0!  C.   H.   MORRISON  &  CO., 

Terms  :  Cash.                                                  1854  PENN  AVENUE. 

2  {yu..  a.j}.^t^,  @   $0.76 

3  da^.  tqcfo.,        @          .26 

/ 

60 
76 

2  6~U.  (Cauv,     @        6. 60 

/3 

00 

26 

16 

Observe  that  this  bill  shows :  (1)  the  jplace  and  the 
date;  (2)  who  hought  the  goods;  (3)  who  sold  the 
goods;  (4)  the  name  of  the  goods  sold  and  the ^rzce  and 
the  amount  of  each  sale. 

The  abbreviation  @  for  ^^  at  *'  should  always  be  used 
in  making  out  a  bill. 

To  foot  a  bill  means  to  add  the  cost  of  all  the  separ- 
ate articles. 

The  word  total  means  the  amount  of  the  sales. 

Make  bills  of  the  following  sales,  using  a  schoolmate's 
name  as  purchaser,  and  your  grocer  as  the  one  who  sells 
the  goods. 

1.  2  lb.  butter,  @  25^ 
6  lb.  meat,  @  15^ 
3  bars  soap,  @  10^ 


178  FOURTH  YEAR  [Written 


2. 


4. 


5. 


6. 


7. 


8. 


9. 


10. 


FOURTH   YEAR 

[ 

b  bills  as  suggested  on  previous  page. 

3  skeins  yarn,  @ 

$0.08 

4  papers  needles,  @ 

.05 

6  yd.  ribbon,  @ 

.50 

5  bu.  potatoes,  @ 

$0.75 

3  boxes  peaches,  @ 

1.50 

12  doz.  lemons,  @ 

.40 

4  spools  thread,  @ 

$0.05 

6  papers  pins,  @ 

.10 

5  cards  hooks  and  eyes,  @ 

.02 

5  lb.  roast  beef,  @ 

$0.15 

3  lb.  pork  chops,  @ 

.15 

4  lb.  lamb  chops,  @ 

.18 

7  silver  forks,  @ 

$2.00 

3  sterling  spoons,  @ 

1.75 

4  napkin  rings,  @ 

3.25 

4  nickel  sponge  racks,  @ 

$2.25 

5  hairbrushes,  @ 

2.00 

6  nickel  towel  rods,  @ 

.75 

4  doz.  linen  writing  paper,  @  $0.20 

4  doz.  linen  envelopes,  @ 

.15 

12  stamps,  @ 

.02 

12  pkgs.  flax  seed,  @ 

$0.05 

3  oz.  cologne,  @ 

.10 

5  lb.  paint,  @ 

.20 

2  music  cabinets,  @ 

$15.00 

5  rocking  chairs,  @ 

5.00 

3  medicine  cabinets,  @ 

3.00 

Oral  and  Written]  MEASURES  179 

REVIEW  OF   MEASURES 

1.  Give  the  table  used  for  measuring  liquids. 

2.  Name  some  articles  sold  by  liquid  measure. 

3.  Give  the  table  used  for  measuring  dry  and  bulky 
articles. 

4.  Name  the  most  common  articles  sold  by  the  peck 
or  the  bushel. 

5.  Give  the  table  of  measures  of  weight. 

6.  Name  the  most  common  articles  sold  by  the  ounce; 
the  pound  ;  the  ton. 

7.  Give  the  table  used  for  measuring  time. 

8.  Give  the  table  of  measures  of  length.  What 
measures  are  used  for  measuring  short  distances?  long 
distances  ? 

9.  Give  the  table  of  measures  of  surface. 

10.  Write  the  names  of  the  measures  on  blackboard 
or  paper,  and  write  each  of  the  following  under  its 
proper  measure :  oil,  cheese,  oats,  hay,  beans,  potatoes, 
coal,  cloth,  molasses,  sugar,  rice,  the  surface  of  the 
blackboard,  the  width  of  the  room,  the  length  of  the 
blackboard. 

11.  Draw  a  diagram  to  show  the  number  of  square 
inches  in  an  oblong  4  in.  by  3  in. 

12.  Show  by  diagram  that  9  square  feet  equal  one 

» square  yard. 
13.    Show  by  a  diagram  on  a  scale  of  -^  inch  to  the 
foot  that  144  square  inches  equal  one  square  foot. 


180  rOUETH  YEAR  [Written 

MEASURES 

Change : 

1.  16  pt.  to  gallons.  8.  74  pk.  to  bushels. 

2.  24  bu.  to  pecks.  9.  3750  yd.  to  feet. 

3.  3  sq.  ft.  to  sq.  inches.     10.  3  in.  to  feet. 

4.  17  yd.  to  feet.  11.  6  mi.  to  rods. 

5.  120  ft.  to  inches.  12.  360  ft.  to  yards. 

6.  50  lb.  to  ounces.  13.  4860  in.  to  feet. 

7.  6  T.  to  pounds.  14.  6966  sq.  ft.  to  sq.  yd. 

15.  How  many  dozen  oranges,  and  how  many  over 
are  there  in  a  box  containing  143  oranges?  165  oranges? 
195  oranges? 

16.  Find  the  number  of  square  inches  in  a  flower  bed 
4  feet  long  and  3  feet  wide. 

17.  The  slate  blackboard  is  3  feet  wide  and  26  feet 
long.     Find  its  surface  in  square  feet. 

18.  A  fruit  dealer  buys  chestnuts  at  $3  per  bushel, 
and  sells  them  at  $.10  per  quart.     Find  his  profit. 

19.  The  schoolroom  floor  is  36  feet  long  and  28  feet 
wide.  Find  the  number  of  square  feet  in  the  floor ;  in 
the  ceiling. 

20.  James  walks  to  school  every  morning,  600  yards. 
How  many  feet  does  he  walk  each  day,  in  going  to  and 
coming  from  school? 

21.  A  huckster  sells  10  bushel-crates  of  peaches  at  20 
cents  per  quarter  peck.  Find  the  amount  from  the  sale 
of  the  peaches. 


Written] 


PRACTICAL  WORK 


181 


I 


I 


PRACTICAL  WORK 

240  ft 

it 

t 

o 

O 

■"^ 

^ 

^ 

^ 

-c 

5 
1 

B 

C 

D 

E 

'  1 

S>i 

Q) 

•< 

^ 

^^ 

5 
CO 

5 
to 

30ft 

40  ft 

40  ft 

40  ft 

40ft. 

50ft 

Sidevs/alk     lOft 

MAIN  STREET 


Tl 


1.  Mr.  Stokes,  a  real  estate  agent,  purchased  this 
plan  of  lots  at  $70  per  front  foot  on  Main  Street.  Find 
the  cost  of  the  plan  of  lots. 

2.  Mr.  R.  M.  Holland  purchased  lot  A  at  $110  per 
front  foot,  and  built  on  it  a  house  for  $6450.  Find  the 
cost  of  Mr.  Holland's  property. 

3.  Mr.  Remington  purchased  lots  B  and  C  for  $8000. 
He  put  an  iron  fence  around  his  lots  at  $1.10  per  foot. 
Find,  the  cost  of  the  fence. 

4.  The  concrete  sidewalk  on  Main  St.  is  10  ft.  in 
width.  Find  the  cost  of  Mr.  Remington's  walk  at  19^ 
per  square  foot. 

5.  Mr.  Stokes  sells  lots  D,  E,  and  F  to  L.  F.  Holtz- 
man  for  $9500.     Find  his  profits  on  these  lots. 


182 


FOURTH  YEAR 


[Written 


Divide  and  test : 
a 

1.  16434  by  64 

2.  34643  by  28 

3.  19603  by  88 

4.  94432  by  62 

5.  26341  by  74 

6.  36236  by  37 

7.  42624  by  41 

8.  76342  by  36 

9.  64283  by  24 

10.  55022  by  82 

11.  44302  by  74 

12.  16792  by  81 

13.  28644  by  73 

14.  74305  by  37 

15.  83265  by  87 

16.  78325  by  75 

17.  85679  by  41 

18.  39410  by  52 

19.  80624  by  68 

20.  73102  by  74 

21.  81103  by  85 

22.  77777  by  96 

23.  88888  by  72 


REVIEW 

b 

28792  by  270 

75639  by  770 
66041  by  602 
77006  by  784 
60424  by  603 
90328  by  735 
76028  by  344 
84605  by  766 
16248  by  860 
74637  by  450 
68026  by  360 
84132  by  770 
70066  by  880 
50468  by  480 
66399  by  790 
24166  by  670 
12345  by  154 
67890  by  221 
89765  by  336 
43210  by  742 
34786  by  819 
57602  by  745 
80703  by  613 


33467  by  890 
77304  by  860 
44384  by  280 
35690  by  761 
88762  by  892 
56044  by  883 
76428  by  444 
23688  by  985 
55624  by  666 
34632  by  555 
99240  by  461 
36002  by  880 
45676  by  390 
76324  by  302 
25321  by  440 
65436  by  784 
70504  by  621 
62131  by  905 
88776  by  860 
54340  by  408 
82107  by  329 
62434  by  752 
93785  by  607 


Written] 


EEVIEW 


188 


» 


PAID    ADMISSIONS    TO    A    FAIR 


TICKETS 

Price 

TUES. 

Wed. 

Thubs. 

Fri. 

Total 
Receipts 

Children 
Adults 

One-horse  vehicles 
Two-horse  vehicles 

15^ 
50^ 

864 

2864 

376 

212 

1865 

3245 

364 

216 

1226 

2764 

176 

144 

1285 

3768 

472 

224 

IV     24.    Find    total    admissions  of    each   class,  and  the 
receipts  in  money  from  each  in  the  4  days. 

25.  Find  the  receipts  in  money  each  day. 

26.  Add  daily  receipts;  add  total  receipts  for  each 
class. 

27.  A  dealer  pays  $  312.50  for  25  children's  bicycles. 
How  much  is  that  apiece? 

28.  A  merchant  pays  $  17.28  for  4  dozen  boys'  caps. 
Find  the  cost  of  each  cap. 

29.  At  $  84  per  dozen,  how  much  does  a  jeweler  pay 
for  15  watches  ? 

30.  A  concrete  walk  80  ft.  long  and  4  ft.  wide  costs 
$  57.60.     How  much  is  that  a  square  foot? 

31.  A  ranchman  clipped  4|-  pounds  of  wool  on  an 
average  from  each  of  2175  sheep.  How  much  is  it 
worth  at  40^  per  pound? 

32.  John's  books  weigh  2|-  lb.,  and  he  weighs  58^  lb. 
How  much  does  he  weigh  with  the  books  in  his  hand  ? 

33.  There  are  1232  pupils  in  a  school,  and  fare  girls. 
Find  the  number  of  girls  in  school ;  the  number  of  boys. 


■ 


184  FOURTH  YEAR  [Written 

34.  A  student  buys  a  dictionary  for  $15,  paying  50>^ 
down,  and  the  balance  in  weekly  installments  of  25^. 
How  many  weeks  will  it  take  to  cancel  the  debt? 

35.  James  picked  4  bu.  3  pk.  of  berries,  and  sold 
them  at  8^  a  quart.     How  much  did  he  receive? 

36.  A  lamp  in  a  lighthouse  consumes  2  gallons  1 
quart  of  oil  daily.  Find  the  cost  of  the  oil  for  Septem- 
ber, October,  and  November  at  18^  per  gallon. 

37.  Make  out  the  bill  for  the  following:  3  pk.  of 
potatoes  at  20^  a  peck,  12  lb.  of  sugar  at  7^  a  pound, 
5  qt.  of  molasses  at  15^  a  quart,  2  lb.  of  cheese  at 
25^  a  pound.  How  much  change  should  be  received 
from  $5? 

38.  A  dealer  buys  three  paintings  at  auction  for 
S  544.  If  he  sells  one  for  $  250,  another  for  $  275,  and 
the  third  for  $375,  how  much  does  he  gain? 

39.  Find  the. cost  of  2  bushels  2  pecks  of  nuts  at  15 
cents  a  peck. 

40.  In  one  season  a  pear  orchard  of  384  trees 
averaged  If  bu.  of  pears  to  the  tree.  Find  their  value 
at  $  1.25  a  bushel. 

41.  How  much  do  I  gain  on  a  box  of  fine  soap  cost- 
ing $  1.80  and  containing  a  dozen  cakes,  if  I  sell  the 
soap  at  20)2^  a  cake? 

42.  A  building  lot  144  feet  long  is  J  as  wide. 
How  wide  is  it  ?     How  many  square  feet  does  it  contain  ? 

43.  Find  the  cost  of  3  bu.  of  cherries  at  6^  a  quart. 


Written]  REVIEW  185 

44.  There  are  30  passengers  seated  and  13  standing 
in  a  car,  in  which  the  conductor  has  collected  $  4.15  in 
5^  fares.     How  many  people  have  left  the  car? 

45.  An  oblong  field  is  80  rods  long  and  25  rods  wide. 
How  many  rods  of  fence  will  it  take  to  inclose  it? 

46.  How  many  square  yards  are  there  in  the  floor  of 
a  room  18  feet  long  and  15  feet  wide? 

47.  In  Ex.  46  find  the  perimeter  of  the  room  in  yards; 
in  feet;  in  inches. 

48.  A  newsboy  buys  Leaders  at  the  rate  of  5  for  3^, 
and  News  at  the  rate  of  7  for  10^.  How  much  does  he 
gain  on  the  sale  of  65  Leaders  at  1^  each,  and  35  News 
at  2^  each? 

49.  Find  the  perimeter  in  feet,  and  the  area  in  square 
inches,  of  an  oblong  26  inches  long  and  18  inches 
wide. 

50.  By  selling  a  horse  for  $  260,  I  lost  $  35.  How 
much  should  I  have  gained  by  selling  it  for  $310? 

51.  A  lady  bought  4  pairs  of  kid  gloves  at  $1.50  a 
pair,  18J  yd.  of  cambric  at  15^  a  yard,  8  yd.  of  muslin 
at  12^^  a  yard,  and  |-  dozen  linen  napkins  at  $4  a 
dozen.     Find  the  cost  of  all. 

52.  The  population  of  the  United  States  increased 
from  9,633,822  in  1820  to  84,907,156  in  1906.  Find 
the  increase  in  this  time. 

53.  A  boy  earns  $  1.25  each  working  day,  and  his  ex- 
penses are  S  4.25  a  week.     Find  his  profits  in  4  weeks. 


PART  lY  — FIFTH   YEAR 
FRACTIONS 

Review  Pages  107,  108,  147,  54,  55,  148  to  152,  119,  120,  156  to  160, 
132  to  137,  163  to  170,  and  172  to  182. 

Fractional  equivalents  of  halves,  fourths,  and  eighths. 
1  unit  =  |. 


1  unit  =  |. 


1  unit  =  |. 


J^^^ 

'V8\ 

/'/6\ 

^^ 

i       =       I       =       I 

1.  The  first  circle  is  divided?  into  how  many  equal  parts  ? 
What  is  each  part  called  ? 

2.  The  second    circle  is   divided   into   how  many  equal 
parts?     What  is  each  part  called  ? 

3.  The  third  circle  is  divided  into  how  many  equal  parts  ? 
What  is  each  part  called  ? 

4.  \  of  the  first  circle  =  |  of  the  second  circle.     \  of  the 
first  circle  =  |  of  the  third  circle. 

5.  How  many  halves  of  a  circle  are  there  in  one  circle  ? 
how  many  fourths  of  a  circle  ?  how  many  eighths  of  a  circle  ? 

6.  Change  \  to  fourths  ;  thus,  J  =  |. 

7.  Change  \  to  eighths ;  J  to  eighths. 

8.  How  many  units  are  there  in  f '  I'  f  ^ 

9.  \  of  the  first  circle  4-  |  of  the  first  circle  =  how  many 
times  the  first  circle  ?     Then  l  +  l  =  how  many  ? 

186 


FRACTIONS  187 

10.  J  of  the  second  circle  +  ^  of  the  second  circle  =  what 
part  of  the  second  circle  ?     Then  -J  +  |  =  how  many  ? 

11.  I  of  the  second  circle  +  |  of  the  second  circle  =  how 
many  times  the  second  circle  ?     Then  |  -f- 1  =  how  many  ? 

12.  I  of   the  third  circle  =  |  of  the  same  circle.     Then 

4  _  ?  _  ? 
^  -  2  -  1- 

J-'i.    :f  — -J  J    2  —  "5  —  1* 

14.  Change  |  and  |  each  to  eighths. 

15.  I  of  an  orange  =  |  =  |^  of  the  same  orange. 

16.  VoMT  boys  each  have  $^.   How  many  dollars  have  they  ? 

17.  .i;i+ii  =  f|;  ||+f^i=||;   iday  +  l  day  =  |  day. 

18.  if  +  i  J  =  8  J  ;  $1  =  how  many  dollars  ? 

19.  I  days  =  — days  ;  |  days  =  1  day  and  |  days. 

20.  ij  +  IJ  =  it;  ij  +  ^i-  +  i^  +  ^|  =*!• 

21.  Write  in  order  of  their  size  ^  of  the  first  circle  ;  |  of 
the  second  circle,  and  |  of  the  third  circle. 

A  unit  is  any  one  thing. 

A  fraction  is  one  or  more  of  the  equal  parts  of  a  unit. 

22.  Write  in  figures  one  half  ;  one  fourth.  How  many 
figures  are  needed  to  express  a  common  fraction  ?  In  the 
fraction  |  what  does  the  4  show  ?  the  3  ? 

23.  ReadJ;  J;  |;  |;  f;  f;  ^. 

24.  Write  seven  eighths  ;  thirteen  twenty-fourths. 

The  denominator  of  a  fraction,  which  is  written  below  the 
line,  shows  into  how  many  equal  parts  the  unit  is  divided. 

The  numerator  of  a  fraction,  which  is  written  above  the 
line,  shows  how  many  equal  parts  of  the  fraction  are  taken. 

The  terms  of  a  fraction  are  the  numerator  and  denominator. 

Fractions  are  said  to  be  equivalent  when  they  have  the 
same  value.     Thus,  ^,  |,  and  |  are  equivalent  fractions. 


188 


FIFTH   YEAR 


Fractional  equivalents  of  thirds,  sixths,  and  ninths. 
1  unit  =  |.  1  unit  =  |.  1  unit  =  |. 


1.    Into  how  many  parts  is  the  first  circle  divided  ?  the 
second  circle  ?  the  third  circle  ? 


1  of  a  circle  =  |  of  the  circle  =  |  of  the  circle. 


I  of  a  circle  =  J  of  the  circle 


of  the  circle. 


|-  of  a  circle  =  J  of  the  circle  =  |  of  the  circle. 

1j_2_?.    l4.3_?.     Ir3_? 
3^6~6>     3^9—9'     3^6  —  6* 


6.  J  of  an  hour  +  J  of  an  hour  =  |  of  an  hour. 

7.  I  of  a  day  +  |  of  a  day  =  |  of  a  day. 

®-      3  +  6~  '3  +  9~  >2+6~  '4  +  8=" * 

9.    Add|  +  l  +  i;    I  +  I  +  I4-I  +  I  +  I;    1  +  1. 

10.  Draw  an  oblong  and  show  that  ^  of  the  oblong  =  f  of 
the  oblong  =  f  of  the  oblong. 

11.  Change  to  equivalent  fractions  in  eighths :    J,  J,  |,  |. 

no      1—1.    2.-1.    2_1.8_? 
"^^-      3~6»    3"~6'     3~"9'    ?~"8' 

13.  How  many  fourths  of  a  pie  =  |  of  a  pie  ? 

14.  Draw  squares  and  show  that  ^  =  ^  ;    that  f  =  f  ;    that 
J  =  f;that|  =  f. 

15.  How  many  halves  equal  one  unit  ?   how  many  thirds  ? 
how  many  fourths  ?   how  many  sixths  ?   how  many  ninths  ? 

16.  I  =  how  many  units  ?    ^=  how  many  units  ?    |  =  how 
many  units  ?     |  =  how  many  units  ? 


FRACTIONS  189 

Fractional  equivalents  of  the  yard  and  the  foot,  and  their 
sum. 


One  foot.  One  yard. 

1.  A  foot  is  what  part  of  a  yard  ? 

2.  2  feet  are  what  part  of  a  yard  ? 

3.  Into  how  many  parts  is  the  yard  divided  ? 

4.  How  many  feet  equal  ^   of  a  yard?     |  of  a  yard? 
I  of  a  yard  ? 

I      5.    Measure  a  yard  on  the  blackboard.     Divide  the  yard 
into  feet.     Divide  a  foot  into  inches. 

6.  How  many  inches  equal  |^  of  a  foot?    |  of  a  foot? 
I  of  a  foot  ?     11  feet  ?     21  feet  ? 

7.  6  inches  are  what  part  of  a  foot  ?   of  2  feet  ?   of  a  yard  ? 

8.  4  inches  are  what  part  of  a  foot  ?   of  2  feet  ? 

9.  llft.  +  ljft.=  —ft. 

11.  1 J  ft.  +  1  ft.  =  how  many  ft.  ?     1|  +  J  =  —      • 

12.  iyd.  +  iyd. +Jyd.=  —  yd.  =— ft. 

13.  21  ft.  +  3|  ft.  =  —  ft.  =  —  yd. 

14.  |ft.  +  ift.=  —ft.;  |ft.4-|ft.+|ft.=  —ft. 

15.  I  ft.  =  —  ft.  ;  I  ft.  =  —  ft.  ;  f  ft.  =  —  ft. 

Add: 

16.  2f  in.  17.    5|  yd.  18. 

H  in.  81yd. 

20.    3^  ft.  21.    7J  yd.  22. 

2f  ft.  61  yd. 

31  ft.  5J  yd. 


19.       2J  ft. 

8|ft. 

2fft. 

J  ft. 

23.     lO^ft, 
lof  ft. 
20^  ft. 

190 


FIFTH  YEAR 


Fractional  equivalents  of  fifths,  tenths,  and  fifteenths,  and 
their  sum  and  difference. 


1  unit  =  |. 


1  unit  =  1^.  1  unit  =  if. 


i 


_2__ 

10 


1.  Into  how  many  parts  is  the  first  circle  divided  ?  the 
second  circle  ?  the  third  circle  ? 

2.  Observe  the  parts  of  each  circle  that  are  not  shaded. 

■J    9      9 

6  -  10  -  T"^- 

3.  Then  |  =  ^^^  =  ^^^  ;  f  =  iV  =  iV  »  I  =  iV  =  l^- 

4.  Each  of   five   boys  had  ^   of   a  dollar.     How  many 
dollars  did  they  have  ? 

5.  What  is  meant  by  J  of  a  circle  ?  |  of  a  circle  ?  |  of  a 
circle  ?  -^^  of  a  circle  ?  -j^  of  a  circle  ? 

6.  f  of  a  circle  +  f  of  the  same  circle  =  |  of  the  circle. 


Then|  +  |  =  |;  t-f  =  i;^-f  =  |. 

7.    How  many   parts  of  a  unit  are  there  in  "1+ ^  +  3-? 
in|  +  |?in32_  +  _5^  +  _.^Mn,3^  +  ,^  +  ^3_?in^8^-^;? 


8.  4  +  ^V=^V;  i  +  TV=i%;  i  +  i 


15- 


9.  1  +  1  =  1?     Then  ^  =  how  many  units  ? 

10.  I  =  how  many  units  and  f  remaining  ? 

11.  ^^  =  how  many  units  and  |  remaining  ? 

12.  If  =  how  many  units  and  ^^  remaining  ? 

13.  Change  to  units  and  parts  of  units :  |,  |,  ^,  -J-J-. 


If  Add; 

14.  12^ 


M 


18.   241  mi. 

41|  mi. 

Subti'act : 

H 

2tV 


I 


22. 


FRACTIONS 


15.   25|  mi. 


19.  1231 
3U 


23.  25i  hr. 


16.    111^ 


20.  50| 


4| 


24.   il4f 


191 


17.    5^^ 

4i 


21.  24Jda. 


3|  da. 


25.   78f  min. 
42^V  min. 


Fractional  equivalents  of  halves,  fourths,  and  sixteenths, 
and  their  sum  and  difference. 


1  unit  =  |. 


1  unit  =  |. 


1  unit  =  1|. 


B 

■ 

^ 


I 


T^ 


1.  How  do  these  three  units  compare  in  size  ? 

2.  Into  how  many  parts  is  the  first  square  divided  ?  the 
second  square  ?  the  third  square  ? 

3.  I  of  the  first  square  =  —  fourths  of  the  second  square 
=  —  sixteenths  of  the  third  square. 

14.    I  =  — units  ;  |  =  — units ;  |  =  — units ;  |f=  —  units* 
5.   2=i=i  =16' 


6-    i=l 


16  ' 


Iff- 


)2 

FIFTH   YEAR 

■>■    1=1  = 
8-    f=TV  = 
9.    i+i  + 

16  5 

_  ? . 

- 1' 

4  = 

O                9                 9 

4  ?    ?  .    6 

5-16-2'   I 

A 

tV  =  f 

=  \&  >  i°5  -  i  = 

_  1 

Add: 

10.  SJft. 
61ft. 
2Jft. 
3|ft. 

11.  16J    ft. 

20J    ft. 
17J    ft. 
10^  ft. 

12.    12{ 

10| 
12J 

13. 

10| 

6| 
8^ 

Subtract : 

14.  «12J 
8i 

15.  28|    yd. 

ISjL  yd. 

16.  18|    mi. 
9^2^  mi. 

17. 

68| 

18.  A  flower  bed  is  4  ft.  6  in.  long  and  3  ft.  4  in.  wide. 
Find  the  distance  around  it. 

19.  The  school  ground  is  in  the  form  of  a  square,  13 J  rd. 
on  a  side.     Find  the  distance  in  rods  around  it. 

Fractional  equivalents  of  sixths,  twelfths,  and  eighteenths, 
and  their  sum  and  difference. 


1  unit  = 

=  l  =  ii 

=  \ 

!• 

'/3 

'/l2 

'/l2 

'/,2 

'Az 

Via 

'/,8 

Vm 

'/la 

'Aa 

'Aa 

yi2=y3 


^/,a=y3 


1.    Into  how  many  thirds  can  the  oblong  be  divided? 
into  how  many  twelfths?  into  how  many  eighteenths? 


I 


FRACTIONS  198 

9      1  —  JL  —  _?    •    2  _  _?_  _  _? 
^-      3  —  12  "~   1^'    3  "~  12  ■"  1^- 

3.  I  of  a  day  =  how   many  9ths  of   a   day?  how  many 
8ths  of  a  day  ? 

4.  1  hour  =  ^2  of  an  hour ;  =  -^^  of  an  hour. 

5.  Change  to  18ths :   J,  |,  |. 

6.  Change  to  16ths :  J,  |,  f . 

7.  I  =  how  many  units?     ^^-  =  how  many  units? 

8.  Change  to  3ds :  ■{-^,  f ,  ||,  f . 

9.  Draw  oblongs  and  show  that  J  =  | ;   |  =  J  ;  i^g  =  J  5 


il  =  f;  ^\^i- 

10.    1|  =  how 

many  units? 

2  0  _  ^Q^  man^ 

^  units  and  ^^^ 

remaining? 

11.    Change  to  units  and  parts  of  units :  |, 

|.  \h  if.  If 

I.  ¥.  ¥'  ii 

Add: 

12.  29J 

32i 

45A 

13.     7tV 

lOf 

25J 

14.  39| 

42A 
28i^ 

15.     5| 

12^ 

16.  27|    ft. 

17.  16^    mi. 

18.  U\  bu. 

19.  12J    da. 

45|    ft. 
25,%  ft. 

29^  mi. 
31J    mi. 

19^  bu. 
16|  bu. 

10^    da. 
18,^  da. 

Subtract : 

20.    ^ 

1      ^ 

21.  17| 

22.  14| 

12tV 

23.  32^ 

30J 

24.    7|  in. 

2S.     9f    bu. 

26.  lOJ  lb. 

27.  15|J  da. 

6,^  in. 

1^  bu. 

6,^  lb. 

5|     da. 

194 


FIFTH   YEAR 


Fractional   equivalents   of   sixths,  twelfths,  and   twenty- 
fourths,  and  their  sum  and  difference. 


1  unit  =  Jl 


i2 
'12 


24 


'/6 

'/6 

'A2 

7/2 

//2 

'Az 

^As^/e 

•/24 

y24. 

y^A. . 

^4 

y24. 

y24. 

^4 

y24. 

Y4*=y6 

1.  What  part  of  the  oblong  =  f  of  it  ?  ^^  of  it  ?  if  of  it  ? 

2.  J  of  the  oblong  =  y^  of  the  oblong;  equals  ^-^  of  it. 

3.  ^  of  the  oblong  =  |  of  the  oblong  ;  equals  -j^  of  it. 

4.  1+1  +  1  +  1=6'    equals  how  many  units ? 

5.  Any  unit  can  be  divided  into  how  many  halves?  3ds? 
4ths?  5ths?  6ths?  7ths?  8ths?  16ths?  24ths,  etc.? 

6.  Add  I  and  -^^  ;  -^^  and  ^^.     From  f^  take  ^V* 

7.  From  If  subtract  J  ;  t^  ;   f  ;  i^. 

8.  I  means  that  a  unit  (|)  and  a  part  of  a  unit  (|)  have 
been  added.     What  does  |  mean  ?  §  ? 

Add: 

10.    154    bu.       11. 


9.    181-    in. 
20^V  in- 


39^1 


m. 


27  J^  bu. 
4ll j  bu. 


Subtract : 
13.      91    yd. 


14. 


14* 


da. 


19J 

20^ 


IS.    28^2 


12.  40^5 
30,V 
18* 


16.   39f 

lis. 


FRACTIONS  195 


REDUCTION  OF  FRACTIONS 


1.  Notice  in  the  diagram  on  p.  30  that  J  =  ^^.  By  what 
number  are  both  numerator  and  denominator  of  -J-  multiplied 
to  change  it  to  -^^  ?  Is  there  any  difference  in  value  between 
i-  and  -^-^  ?  Notice  that  the  terms  in  ^-^  are  larger  or  higher 
than   in  J.     The   change  of   J  to  the  equal  fraction  ^^  is 

Ifcalled  changing  or  reducing  J  to  higher  terms. 

2.  By  what  number  must  both  terms  of  i^^  be  divided  to 
change  g*^  to  i  ^  Is  there  any  difference  in  value  between 
2*^  and  i  ?  Which  fraction  has  the  lower  terms  ?  The 
change  of  ^^  to  \  is  called  reducing  -^^  to  lower  terms. 

3.  Notice  in  the  diagram  that  /^  =  t2  =  6  •  When  ^^  is 
changed  to  ^2_  it  is  reduced  to  lower  terras  but  not  to  its 
lowest  terms,  since  -^  can  be  changed  to  still  lower  terms,  J. 
Can  1  be  reduced  to  still  lower  terms  ?  The  change  of  -^^ 
to  J  is  called  reducing  -^-^  to  its  lowest  terms. 

4.  By  what  number  must  both  terms  of  |-  be  multiplied 
to  change  it  to  the  equal  fraction  J?  By  what  number 
must  both  terms  oi'^-Q  be  divided  to  change  it  to  the  equal 
fraction  |?     Is  |  in  its  lowest  terms  ? 

Multiplying  or  dividing  both  terms  of  a  fraction  by  the  same 
number  does  not  alter  its  value, 

5.  Reduce  to  higher  terms  :  | ;  |  ;  | ;  f  ;  | ;  |  ;  f  ;  yo  • 

6.  Reduce  to  lowest  terms  :  |  ;  | ;   | ;  -f ;   ^^  '■>  -f^. 
Fractions  like  -J,  |,  and  |,  which  have  the  same  denomina- 
tor, are  said  to  have  a  common  denominator. 

Similar  fractions  are  fractions  tliat  have  a  common  denom- 
inator. 

7.  Change  to  similar  fractions  ^  and  | ;  ^  and  J ;  ^  and  -^^ ; 
|,  j,  and  |. 


196  FIFTH  YEAR 


Written  Work 

1.  Change  f  and  |  to  similar  fractions  having  the  common 
denominator  12. 

Since  the  denominator  3  in  |  must  be  multiplied  by  4 
2x4        8       to  produce  12,  the  numerator  must  also  be  multiplied  by 

o  X  4       lZ     4,  so  as  not  to  change  the  value  of  the  fraction.    ^     a.=  19' 

3x3        9       Cilice  the  denominator  4  in  |  must  be  multiplied  by  3  to 

A  v^  Q  ~  To     produce  12,  the  numerator  3  must  also  be  multiplied  by  3. 

3x3      9 

-     o  =  7^-     Hence  the  similar  fractions  are  A  and  A. 

4  X  3      12  12         T^ 

Change  to  similar  fractions : 

2.  J  and  I      4.    I  and  |       6.    l  |,  and  |      8.    J,  |,  and  -^-^ 

3.  I  and  I      5.    I  and  \       7.    |,  J,  and  f      9.    f ,  f,  and  ^^ 

10.  Reduce  ^^  to  its  lowest  terms. 

g_j_Q       9      2  —  2       1  ^^  ^^^  divide  both  terms,  6  and  24,  of  the 

^TT  ^   Q  =  Q»    o   .   9^^T       fraction  /j  by  3  without  changing  the  value 
*^      *  '   *^  of  the  fraction.     The  result  is  f.     We  can 

then  divide  both  terms  2  and  8  of  the  fraction  2  by  2.     The  result  is  \. 

Reduce  to  lowest  terms : 

11.  i^  13.    If  15.    If  17.     If  19.     1| 

12.  -/^  14.     ^%  16.     1^  18.     If  20.     if 

21.  Change  |^  to  units.  Thus,  1  unit  =  2  halves.  In 
4  halves  there  are  4  -^  2,  or  2,  units.     Change  IgO-  to  units. 

22.  Change  ^-  to  units  and  parts  of  units.  Thus,  1  =  3 
thirds.  In  10  thirds  there  are  10  -^  3,  or  3,  units  and  J  re- 
maining;  that  is,  3  J. 

To  cJiange  a  fraction  to  units  and  parts  of  units  ^  divide  the 
numerator  hy  the  denominator. 

Change  to  units  and  parts  of  units  : 

23.  Y  24.     -I32.  25.     Jg^-  26.     ^^-  27.    J^ 


FRACTIONS  197 

ADDITION  OF  FRACTIONS 

1.    Can  you  add  J  and  J  without  change  ?    Can  you  add 
fj  and  ^  ?  What  change  must  be  made  in  J  and  J  before  they 
5an  be  added  ? 

2-     ^  — TO'    5  — TXT'    f  —  1X>»    5—10- 

o        1_     ?    .     Ill—     ?    .     111  —  ?.     l_l_l_?? 

4.  Can  you  add  \  and  J  without  change?  Change  both 
[to  tenths.     Can  they  then  be  added  ? 

5.  Can  you  add  \  and  \  without  change  ?  Change  both 
to  sixths.     Can  they  then  be  added  ? 

6.  When  I  and  \  are  to  be  added,  to  what  similar  fractions 

•should  they  be  changed  ? 

7.  What  are  the  denominators  of  the  fractions  in  exam- 
ple 4?  To  what  like  or  common  denominators  (c.  d.)  did 
you  change  both  fractions  ? 

8.  What  are  the  denominators  of  the  fractions  in  example 
5  ?  To  what  denominator  did  you  change  the  fraction  |^  ?  J  ? 
Why? 

9.  After  two  or  more  fractions  are  changed  to  like,  or 
common  denominators^  that  is,  after  they  have  been  made 
similar^  what  is  the  second  step  in  adding  them  f 

in     Afhliii-    11-    1     ^-     11     1-    11     1 
J.U.    ^(lUg^g,  g,    :j,  ^,     5'  TfT'     3'¥'T2>     3'  ^'  T^* 

11.  Observe  that  in  problem  10,  |^+ J4- i  =  |,  or  1,  and 
thatJ+i+iV  =  A'Orf. 

12.  What  is  the  third  step  in  adding  fractions  ? 
Why  is  the  first  step  not  necessary  in  the  following? 


13-    l  +  J 

"■    i  +  f 

17. 

J  +   f   +   f  +  1 

"•    4  +  f 

16.    f  +  ^ 

18. 

tV  +  tV  +  A  +  -i% 

198  FIFTH  YEAR 

Give  the  sums  at  sight : 
19.    i  +  i  +  i  28.    Jj  +  ^+^j  +  ^ 

20-    i  +  i+i  29.    ^2_  +  _3^4._5^+^^ 


21. 

i  +  i  +  i 

30. 

^+A+A+A 

22. 

l  +  i  +  i 

31. 

tV  +  t'6  +  i\  +  t\ 

23. 

i+l+i+l 

32. 

2V+2V+2'o  +  2V 

24. 

Hf  +  f  +  f 

33. 

A  +  A+iV+A 

25. 

tV  +  t%  +  ^  + 

A 

34. 

2^5+A  +  A+2V 

26. 

iV+iV  +  A 

35. 

tV  +  l\  +  1 V  +  tV 

27. 

Hf+f+l 

36. 

t\  +  tV  +  tV  +  ^ 

37.  A  boy  spent  |  of  his  money  for  a  knife,  ^  of  it  for  a 
ball,  and  ^  of  it  for  his  lunch.  What  part  of  his  money 
did  he  spend  ? 

38.  After  cutting  off  |^  of  a  foot  and  |  of  a  foot  from  a 
bgard,  the  part  remaining  was  |  of  a  foot  long.  How  long 
was  the  whole  board  ? 

39.  I  paid  |Jq  for  milk,  f^2_  f^^  lettuce,  andi^3_  for  but- 
ter.    What  part  of  a  dollar  did  I  pay  for  all  ? 

40.  David  paid  f  of  a  dollar  for  a  fishing  rod,  and  ^  of  a 
dollar  for  a  line.     How  much  did  he  pay  for  both  ? 

Adding  fractions  that  are  not  similar. 

Written  Work 

The  fractions  must  first  be  made  simi- 
lar. They  may  be  changed  to  the  com- 
mon denominator  twelfths.  Multiplying 
both  terms  of  |  by  4  changes  it  to  ^%,  and 
multiplying  both  terms  of  ^  by  3  changes 
it  to  jV    The  sum  of  ^V  and  j\  is  ^^. 

Fractions  must  he  made  similar  before  they  can  he  added. 


1. 

Addf 

and  ^. 

12  =  c, 

.  d. 

2x4 

8 

3x4" 

12 

1x3 

4x8" 

3 
12 

FRACTIONS  199 

Add,  using  a  pencil;  then  orally: 

2.  J  and  J  8.  J  and  1  14.  J  and  J 

3.  I  and  ^  9.  I  and  |  15.  ^  and  1 

4.  J  and  J  10.  I  and  ^  16.  ^  and  J^ 

5.  J  and  ^  11.  ^  and  ^  17.  |  and  ^ 

6.  J  and  ^  12.  |^  and  ^  18.  J  and  i 

7.  I  and  -J-  13.  J  and  ^  19.  J  and  J^ 

20.  Henry  had  J  of  a  dollar,  and  found  |  of  a  dollar. 
How  much  had  he  then? 

21.  Mary  bought  ^  of  a  yard  of  red  ribbon,  |  of  a  yard  of 
blue  ribbon,  and  J  of  a  yard  of  white  ribbon.  How  many 
yards  of  ribbon  did  she  buy  ? 

22.  What  is  the  total  cost  of  a  ball  at  |  of  a  dollar,  a  pen- 
knife at  ^  of  a  dollar,  and  a  book  at  |^  of  a  dollar  ? 

A  mixed  number  is  a  number  expressed  by  a  whole  num- 
ber and  a  fraction ;  as,  5J,  3J,  11^. 

Adding  mixed  numbers  when  the  sum  of  the  fractions  is  less 
than  a  whole  unit. 

Written  Work 
1.    Add  2^  and  3i. 

12  =  c.  d.  ^  and  ^  may  each  be  changed  to  twelfths.     Write 


21       _  2-4-    the  common  denomiuator  (c.  d.),  12,  above  the  frac- 

3  "^12  1x4       41x3       3 

H       =  ^1%    *io^s-     3x4^12'  4x3^  l2*    The  sum  of  the  frac- 


3  "T"     4  12  tions  is  3^2  and  the  sum  of  the  integers  is  5 ;  5  +  ^'^^  =  ^i^* 

Add: 

2.    5J  3.    121 

6i  14J 


H 

5.   35J 

201 

60J 

8iV 

422V 

200 
Add 


6. 


10. 


FIFTH   : 

iEAR 

18tV 

7.    20J 

24i 

28iV 

8.    IIH 

i 

9.     20^ 

145,V 
230J 

lOOJ 

80iV 
205^ 

11.     351 

H 

12.    12J 

13.    128| 
34 

14.  A  man  walked  3^  miles  one  hour,  3J  miles  the  second 
hour,  and  2J  miles  the  third  hour.     How  far  did  he  walk  ? 

15.  A  farmer  sold  corn  for  $  14^,  wheat  for  $  37^,  and  rye 
for  $  15^^Q.     How  much  did  he  receive  for  all  ? 

Adding  mixed  numbers  when  the  sum  of  the  fractions  is 
greater  than  a  whole  unit. 


Written  Work 

1.    Add  8f  and  12f . 

15  = 

12f  = 

c.  d. 
1%^ 

f  and  1  may  each  be  cha 
2x5_10.  3x3_  9 
3x5      15'  5x3      15* 
T»5  is  ^f,  which  equals  l^^s 
to  the  sum  of  12  and  8, 
with  rV  makes  21x*5. 

mged  to  fifteenths. 
The  sum  of  {^  and 
.    The  1  is  added 

8f  +  12|  = 

20l|  or 
21tV 

making  21,  which 

Add: 

2.        7| 

3. 

150f              4. 

m 

5.      321 

!i 

68f 

18f 

60^^, 

6.   175^ 
161 

7. 

350,:^            8. 

267| 

419| 

22J 

9.      17| 

^ 

FRACTIONS 


201 


Add: 
fio.      80J 

181 
42f 

12A 


11. 


17| 
71| 


12.     20| 

120| 

268H 


13. 


1351 

122t^ 

118,V 


14.  Mary  bought  a  reader  for  f  of  a  dollar,  a  slate  for  -^ 
of  a  dollar,  and  a  grammar  for  J  of  a  dollar.  How  much 
did  they  all  cost  ? 

15.  A  clerk  spent  $18 J  a  month  for  board,  i9|  for  a 
room,  and  14^  for  clothes.  How  much  did  he  spend  in  one 
month  ? 

16.  I  sold  J  of  an  acre  of  land  to  one  man,  2^  acres  to  an- 
other, and  If  acres  to  another.     How  many  acres  did  I  sell  ? 

17.  Find  the  perimeter  of  a  sheet  of  paper  9J  in.  by  5J  in. 


SUBTRACTION  OF  FRACTIONS 


'A 

■ 

fi 

B 

i 

1.  1  sq.  in.  —  1  sq.  in  =  —  sq.  in. 

2.  1  sq.  in.  —  ^  sq.  in.  =  —  sq.  in. 

3.  1  sq.  in.  —  :|  sq.  in  =  —  sq.  in. 

4.  I  sq.  in.  —  j4g  sq.  in.  =  —  sq.  in. 

5.  ^  sq.  in.  —  -^q  sq.  in.  =  —  sq.  in. 

6.  |-i  =  i;  f- 


H  '     10 


io  —  ilF* 


202  FIFTH  YEAR 


7.  Give   answers   to   the  following:  y|  — 1^2^    ii— i\; 
t\  ~  1*1  '   2  0  ~  10  »   2 &  ""  2  5- 

8.  What  do  you  notice  about  the  denominators  of  the 
fractions  you  have  subtracted  in  example  7  ? 

In  subtraction  of  fractions,  just  as  in  subtraction  of  whole 
numbers,  the  minuend  must  be  larger  than  the  subtrahend. 

9.  When  the  denominators  are  alike,  what  do  we  sub- 
tract ? 

10.  Could  you  subtract  \  from  J  without  change  ?     How 
may  these  fractions  be  made  similar  ? 

11.  When  the  denominators  are  unlike^  what  is  the  first 
step  9    What  is  the  second  step  P   What  is  the  third  step  ? 

Subtract: 

12.  fj-*i;  I  ft. -J  ft.;  I  yd. -I  yd.;  ^ift.-|ft. 

13-  ^-|;  M-f;  \\-h  \-h  ll-h  \-\- 

Subtracting  similar  mixed  numbers. 
Written  Work 

Since  |  cannot  be  subtracted  from  ^, 
we  take  1  or  |  from  3,  and  add  it  to  ^, 
thus  changing  3^  to  2f .  Tlien  \  from 
I  leaves  |  and  1  from  2  leaves  1.  Hence, 
the  answer  is  If. 


7.  SS^-aj-   5^ 

8.  17if-1.3,\ 

9.  \\\   -  9f 

10.  7f    -   2| 

11.  18f    -  9f 


1. 

From  %\ 

;  take  If. 

^- 

■1|  =  1* 

Find  the  differences : 

2. 

^  - 

H 

3. 

H  - 

^ 

4. 

Hh- 

61% 

S. 

20H-i^H 

6. 

I6M-II2V 

I 


FKACTIONS  203 


I 


12.  If  a  boy  buys  papers  at  f  of  a  cent  each,  and  sells 
them  at  1  cent  each,  how  much  does  he  gain  on  each  paper  ? 

13.  I  bought  a  bushel  of  potatoes  for  -^q  of  a  dollar,  and  a 
bushel  of  corn  for  -f^  of  a  dollar.  How  much  more  did  I  pay 
for  the  potatoes  than  for  the  corn  ? 

14.  William  bought  a  hat  for  $2|,  and  a  pair  of  shoes  for 
^2^.  How  much  more  did  he  pay  for  the  hat  than  for  the 
shoes  ? 

15.  From  a  piece  of  ribbon  16^7^  inches  long  was  cut  a  piece 
J  inches  long.     What  was  the  length  of  the  piece  remaining  ? 

16.  One  farmer  owns  124^^1  acres  of  land,  and  another 
owns  llli%  acres.  How  many  more  acres  does  the  one 
farmer  own  than  the  other? 

Subtracting  fractions  or  mixed  numbers  that  are  not  similar. 
Written  Work 

1.    From  I  take  |.  Before  they  can  be  subtracted  the  fractions 

20  =  c.  d.  must  be  made  similar.    Change  them  both  to 

1  _  1  twentieths,     i  =  ^  and  ^  =  ^.   Subtracting, 

Fractions  must  be  made  similar  before  they  can  be  subtracted. 
Subtract,  using  a  pencil ;  then  orally: 


I 


2-  i-i 

9-    i-i 

16.    J-t1j 

3-    \-\ 

10.    I-} 

17.    i-i 

4-  i-i 

"•    \-\ 

"•    \-\ 

5-  J-i 

12-    i-i 

19.    \-i 

«•  \-\ 

13.    \-\ 

20.    I-tV 

->■   i-T^ 

"•    i-i 

21.    \-\ 

«•    i-i 

"•    i-^ 

22.    t-J 

204  FIFTH  YEAR 

23.  From  a  piece  of  cloth  containing  J  of  a  yard,  ^  of  a 
yard  was  sold.     What  part  of  a  yard  remained  ? 

24.  From  a  city  lot  containing  |  of  an  acre,  -^^  of  an  acre 
was  sold.     What  part  of  an  acre  remained  ? 

25.  A  man  traveled  ^  of  a  certain  distance  the  first  hour, 
and  I  of  the  distance  the  second  hour.  What  part  of  the 
distance  farther  did  he  travel  the  first  hour  than  the  second? 

26.  From  7  take  |. 

7  =  6|  Change  7  into  6f .   Subtracting  |  from 

1—2.  I  gives  I,  which  added  to  6  gives  6^. 

Subtract,  using  a  pencil;  then  orally: 

27.  3-1  34.      22-1^ 

28.  12-2  35.  7_J 

29.  18 -J  36.       28 -ij 

30.  9-|  37.      55 -if 

31.  3-f  38.         4- If 

32.  100 -^9^  39-     125 -J^ 

33.  18 --If  40.       10- I 

48.  Albert  had  $2  and  spent  $|-  for  skates, 
money  had  he  remaining  ? 

49.  A  vessel  contained  8  gallons  of  oil.  After  |^  of  a  gal- 
lon had  leaked  out,  how  much  remained  ? 

50.  A  grocer  who  had  bought  10  bushels  of  potatoes,  sold 
I  of  a  bushel.     How  many  bushels  remained  ? 

51.  From  12|  take  10 J. 

4  =  c.  d.  Change  I  to  fourths,      i  =  |. 

12|  =  12#  I  ^''""^  f  =  i  which  added  to  12 

101  =102  less  10,  or  2,  gives  2^. 

12|-10i=    2i 


41. 

133- 

-1 

42. 

44- 

-A 

43. 

11- 

-f 

44. 

40- 

-f 

45. 

7- 

-i\ 

46. 

51- 

-iV 

47. 

48- 

-i 

.     How  much 

I 


FRACTIONS  205 

Find  differences: 

52.  4f   -    3J  62.      80|   -    14J 

53.  7|    -   41  63.      98f   -    321 

54.  lOf   -    31  64.  45|f-    30f 

55.  101   _    2f  65.  25|   -    12} 

56.  12^   -    5f  66.  1001    _    521 

57.  24f,-llf  67.  78|   -    35f 

58.  3111 -18f  68.  50|-    -    40J 

59.  79i|_26|  69.  1243-\-112i 

60.  9Ti{-35f  70.  24011-2001 

61.  121f   -66f  71.      15|-   -      8i 

72.  From  a  lot  containing  17|  acres,  5|  acres  were  sold. 
How  many  acres  remained? 

73.  One  motorman's  trip  takes  4|  hours,  and  another's  2| 
hours.  How  much  longer  is  the  first  motorman's  trip  than 
the  second  motorman's  trip  ? 

74.  A  man  bought  two  suits  of  clothes,  one  costing  $35| 
and  the  other  i28J.  How  much  more  did  the  one  suit  cost 
than  the  other  ? 

75.  James  lives  1^  miles  from  the  schoolhouse,  and  Sam- 
uel If  miles  away.  How  much  farther  does  Samuel  have  to 
walk  to  school  than  James  ? 

REVIEW 

1.  A  newsboy  earned  If  one  day,  $-^  another  day,  and 
$1  a  third  day.     How  much  did  he  earn  in  the  3  days  ? 

2.  A  stick  was  broken  into  two  pieces  —  one  3|  ft.  long 
and  the  other  1|  ft.  long.     How  long  was  the  whole  stick  ? 

I       3.    If  a  man  earns  1 3|  a  day,  and  a  boy  S|  a  day,  how 
much  more  does  the  man  earn  in  a  day  than  the  boy  ? 


206  FIFTH  YEAR 

4.  What  will  be  the  total  cost  of  1  sack  of  flour  $1|, 
sugar  i^,  dried  beef  1^^^,  and  corned  beef  |i? 

5.  A  boy  is  4  ft.  5  in.  tall.  His  sister  is  3  ft.  5  in.  tall. 
How  much  taller  is  the  boy  than  his  sister  ? 

6.  The  top  of  a  door  is  12|-  feet  above  the  ground,  and 
the  bottom  of  it  is  4|  feet  above  the  ground.  How  high  is 
the  door? 

7.  Four  loads  of  coal  weighed  as  follows:  2  tons,  1|  tons, 
2 J  tons,  and  2J  tons.     How  much  did  the  four  loads  weigh  ? 

8.  The  rainfall  in  April  was  4 Jq  inches,  in  May  3|  inches, 
and  in  June  4^  inches.  What  was  the  total  rainfall  for  the 
three  months  ? 

9.  From  a  barrel  containing  51J  gallons  of  oil,  17|^  gallons 
were  sold  in  one  day,  and  25J  gallons  another  day.  How 
many  gallons  remained  unsold  ? 

10.  A  station  agent  who  was  paid  860  per  month  spent 
in  one  month  il2|  for  groceries,  $7j^  for  meat,  and  |15| 
for  other  expenses.     How  much  did  he  save  ? 

11.  A  farmer  drives  in  one  day  12|  miles,  then  6J  miles, 
and  then  9J  miles.     How  far  does  he  drive  ? 

12.  To  the  sum  of  22|^  and  15J  add  their  difference. 

13.  From  38/^  take  the  sum  of  16 J  and  12i^. 

14.  The  feed  for  a  horse  cost  85|  per  month;  for  a  cow, 
$4:^  per  month.  If  a  man  has  2  horses  and  2  cows,  how 
much  will  it  cost  to  feed  them  a  month  ? 

15.  A  boy  walked  from  his  home  east  along  a  certain  road 
IJ  miles.  He  then  walked  to  a  place  2^  miles  west  of  his 
home.     How  far  had  he  walked  when  he  got  home  ? 

16.  A  man  purchased  a  chair  for  -f  4^,  a  stove  for  $6 J,  a 
table  for  i8J,  and  a  bookcase  for  $12.00.  How  much  did 
they  cost  ? 


FRACTIONS 


20T 


17.  When  a  grocer  receives  a  $10  bill  in  payment  for  sugar 

$|,  vegetables  f  1^^,  fruits  l|,  rice  I  J,  and  cakes  $1^,  how 
much  change  does  he  give  ? 

18.  A  student  in  the  city  in  one  month  paid  1 4^^  for  car 
fare,  1 18 J  for  board,  i7|  for  room,  $2|  for  laundry,  and  $61 
for  books.  How  much  did  his  expenses  amount  to  during 
that  month  ? 

19.  During  the  same  month  he  earned  $30  by  tutoring, 
$18 J  by  selling  books,  and  $12|  by  chemical  work.  How 
much  did  he  have  left  after  paying  expenses  ? 

20.  In  3  days  in  June  the  sun  shone  in  New  York  Ill- 
hours,  14^  hours,  and  14l|  hours.  How  many  hours  of 
sunshine  were  there  in  these  3  days  ?  How  many  hours 
without  sunshine  were  there? 

MULTIPLICATION  OF  FRACTIONS 
Multiplying  a  fraction  by  a  whole  number. 


IT 


IL 


H 


1. 
2. 
3. 
4. 
5. 
6. 
7. 
8. 


3  feet  -  I  yard 

Into  how  many  halves  is  the  square  divided  ? 

Two  times  |-  the  square  = square. 

Two  times  $J=- 
Four  times  $J=- 
Five  times  $J  =  - 


dollar. 
-  dollars. 
•  dollars. 


Into  how  many  feet  is  the  yard  divided  ? 
What  is  one  of  these  parts  called  ? 
What  are  two  parts  called  ? 


208  FIFTH  YEAR 

9.  2  X  J  of  a  yard  = yard. 

10.  6  X  J  of  a  yard  = yards. 

11.  6  X  1^  of  a  circle  = circles. 

12.  12  X  J  of  a  circle  = circles. 

13.  4  X  J  is  the  same  as  |^  +  ^  +  |^  +  J. 

14.  6  X  I  =  |,  or  3.  Therefore  to  multiply  ^  by  6,  we  say 
six  times  |  =  |,  or  3. 

Give  products: 

15.  8  X  J  20.    9  X  f  25.       7  X  f  30.       3  X  ^^^ 

16.  12  X  J  21.     8  X  f  26.    12  X  f  31.    12  X  I 

17.  6  X  I  22.     9  X  -^Q         27.       4  X  -^^        32.       5  X  | 

18.  7  X  I  23.    6  X  I  28.       8  X  f  33.       6  X  f 

19.  10  X  I  24.    8  X  f  29.    11  X  J  34.       6  X  | 

Finding  fractional  parts  of  whole  numbers. 

1.  ^  of  1  unit  = unit. 

2.  J  of  2  units  = unit. 

3.  J  of  12  = dollar. 

We  have  learned  that  we  may  divide  a  unit  into  any  num- 
ber of  parts  and  then  take  any  number  of  these  parts;  thus, 
I  of  $60  means  that  $60  (60  units)  is  divided  into  4  equal 
[>arts  of  $15  each  and  that  3  of  these  parts,  or  845,  are  taken. 


Since!- of  $60  =  $15, 

1  of  $60=3  X  $15,  or  $45. 

Find  the  following: 

4. 

f  of  $24 

8.   1  of  36  minutes     12. 

J  of  72  cents 

5. 

j\  of  60  horses 

9.   11  of  $144              13. 

^\  of  99 

€. 

1  of  36  days 

10.    -f^  of  78  miles        14. 

T%  of  75 

7. 

1  of  20  hours 

11.   -fj  of  44  rods          15. 

f  of  84 

FRACTIONS  20& 

16.  If  I  wish  to  find  J  of  4,  into  how  many  parts  do  I 
divide  4?  How  do  I  find  one  of  these  parts?  Divide 
4  by  3. 

17.  Explain  what  you  mean  by  ^  of  a  number ;  by  |  of 
a  number ;  by  |  of  a  number. 

18.  Find  I  of  4. 

Solution.  —  i  of  4  =  f ,  and  f  of  4  =  2  x  |,  or  |  =  2f 

Find  the  following : 


19. 

|of7 

25. 

T%  of  12 

31. 

f  of  20 

20. 

|of9 

26. 

11  of  8 

32. 

f  of  6 

21. 

|ofl2 

27. 

i\of8 

33. 

iof9 

22. 

|of8 

28. 

|of9 

34. 

f  of  11 

23. 

f  of  10 

29. 

3-  of  12 

35. 

loflO 

24. 

|of3 

30. 

fof7 

36. 

t  of  12 

37.  Multiply  I  by  8.  Which  number  is  the  multiplier? 
Which  number  is  the  multiplicand?  Observe  that  |  of  8 
gives  the  same  result. 

We  find  a  fractional  part  of  a  number  by  partition. 

If  the  sign  of  multiplication  is  written  after  a  fractional 
multiplier,  it  may  be  read  "of."  Thus,  |  X  12  may  be 
read  "f  of  12." 

Read  the  following  problems : 

38.  I  X  9  39.     I  X  6  40.     I  X  4  41.    f  X  6 

Written  Work 

1.  A  merchant  owing  $1200  gave  his  check  for  |  of  the 
amount.     For  how  much  did  he  write  his  check  ? 

2.  Three  men  own  2500  acres  of  land.  The  first  owns  |  of 
it,  the  second  |  of  the  remainder,  and  the  third  the  remainder. 
How  many  acres  does  each  own  ? 


210  FIFTH  YEAR 

3.  If  a  laborer  works  ^  of  the  days  in  a  common  year,  how 
many  days  does  he  work  ? 

4.  A  student's  expenses  at  college  are  $480  per  year.  If 
board  and  tuition  cost  |  of  that  amount,  how  much  is  spent 
for  room  rent,  books,  etc.  ? 

5.  A  contractor  agrees  to  erect  a  building  for  $24,570. 
Labor  costs  J  of  the  amount,  material  J  of  the  remainder. 
Find  his  profit. 

6.  I  of  the  entire  enrollment  of  14,720  in  school  are  girls. 
Find  the  number  of  girls  and  the  number  of  boys. 

7.  -^Q  of  I960  is  paid  in  a  year  for  rent.  Find  the  monthly 
rent  bill. 

8.  An  automobile  cost  $3456  and  the  expenses  and  repairs 
for  one  year  were  -^q  of  the  cost.     Find  the  expenses. 

9.  A  western  farmer  bought  a  farm  of  160  acres  at  $25 
an  acre.  He  erected  a  house  costing  -^^  as  much  as  the 
land,  and  a  barn  costing  ^  as  much  as  the  house.  Find  the 
total  cost  of  the  property. 

Finding  a  number  when  a  fractional  part  of  it  is  given. 

1.  f  of  a  flock  of  sheep  are  40.  Find  the  number  in  the 
flock. 

Solution.  —  Since  two  thirds  of  the  flock  equal  40  sheep,  one  third  of 
the  flock  equals  I  of  40  sheep,  or  20  sheep,  and  three  thirds,  or  the  flock, 
equal  3  x  20  sheep,  or  60  sheep. 

Find  the  number  when  : 

2.  I  of  a  number  =  12  7.    |^  of  a  number  =  12 

3.  I  of  a  number  =9  8.   ^j  of  a  number  =  36 

4.  ^  of  a  number  =  15  9.   ^|  of  a  number  =  60 

5.  I  of  a  number  =  21  10.    |^  of  a  number  =  45 
•6.   f  of  a  number  =  18  11.   -f^  of  a  number  =  54 


FRACTIONS  211 


Written  Work 

1.  There  are  18  girls  in  a  school.  This  number  is  |  of  all 
the  pupils  in  the  school.  How  many  pupils  are  there  in  the 
school ? 

2.  James  deposited  818  in  a  savings  bank,  which  was  |  of 
wliat  he  earned  during  the  month.  How  much  did  he  earn 
in  the  month  ? 

3.  May  spelled  correctly  27  words,  which  were  ^^^  of  all 
the  words  given.     How  many  words  were  given  ? 

4.  A  farmer  sold  42  lambs,  which  were  |-  of  his  flock. 
How  many  lambs  had  he  at  first  ? 

5.  John  has  attended  school  40  days,  which  are  |  of  the 
number  of  days  in  the  term.  Find  the  number  of  days  in 
the  term. 

6.  Mr.  Tanner  pays  $30  each  quarter  for  his  telephone* 
At  the  same  rate,  how  much  does  he  pay  in  a  year  ? 

7.  i500  is  I  of  a  teacher's  salary.     Find  her  salary. 

5  of  the  six  parts  of  her  salary  =  $500. 

1  part  =  1  of  $500,  or  $100. 
6  parts,  or  her  salary  =  6  x  $100  =  $600. 

8.  Mr.  Arnold  bought  a  horse  and  a  cow.  He  paid  850' 
for  the  cow,  which  was  ^  of  what  the  horse  cost.  How  much 
did  they  both  cost? 

9.  A  traveling  salesman  drove  18  miles  one  day.  This, 
was  ^  as  far  as  he  rode  on  a  train.  How  far  did  he  ride  on 
the  train  ? 

10.  The  cost  of  a  barn  was  |  as  much  as  the  cost  of  a 
house.  If  the  barn  cost  8920,  how  much  did  they  both 
cost  ? 


212  FIFTH   YEAR 

11.  The  distance  from  New  York  to  Harrisburg,  Pa.,  ia 
195  miles.  This  is  J|  of  the  distance  from  New  York  to 
Pittsburg.     What  is  the  latter  distance  ? 

12.  A  steel  rail  is  30  feet  long.  This  is  -^^  of  the  length 
of  a  Pullman  car.     What  is  the  length  of  a  Pullman  ? 

Multiplying  a  mixed  number  by  an  integer. 

Analyze  these  problems  : 

1.  Find  the  cost  of  6  eggs  at  3J  cents  a  piece. 

2.  Find  the  cost  of  4  qt.  of  oil  at  4|  cents  per  qt. 

3.  How  much  will  8  lb.  of  rice  cost  at  6J  cents  per  lb.  ? 

4.  Find  the  cost  of  12  lb.  of  sugar  at  6J  cents  per  lb. 

5.  When  berries  are  sold  for  8|-  cents  per  basket,  find 
the  cost  of  6  baskets. 

6.  A  man  earns  $lf  per  day.  How  much  does  he  earn 
in  6  days? 

7.  When  apples  are  sold  for  $1|  per  bushel,  find  the  cost 
of  8  bushels. 

8.  Mary  pays  8|  for  music  lessons  and  takes  two  lessons 
per  week.  How  much  do  her  music  lessons  cost  her  in  4 
weeks  ? 

9.  John  makes  f  of  a  cent  on  each  paper  and  averages 
40  papers  each  day  for  six  days.     Find  his  profit. 

10.  We  pay  7J^  per  qt.  for  milk.  How  much  is  our  milk 
bill  in  4  weeks,  if  we  use  2  qt.  per  day  ? 

Suggestion.  —  Find  the  bill  for  each  day ;  then  for  each  week ;  and 
then  for  the  number  of  weeks. 

11.  By  buying  25  cents  worth  of  street  car  tickets,  each 
ticket  costs  me  4J  cents.     Find  the  cost  of  12  tickets. 


FRACTIONS  213 

12.  A  storekeeper  makes  IJ  cents  on  each  can  of  corn. 
How  much  does  he  make  on  18  cans  ? 

13.  John  works  for  5 J  cents  per  hour.       If  he  works  3 
hours  a  day,  how  much  does  he  earn  m  2  days  ? 

14.  Mary  uses  1|  yd.  of  ribbon  for  a  bow.     How  much 
does  it  take  for  9  such  bows  ? 

15.  Find  the  cost  of  a  dozen  eggs  at  3J  cents  apiece. 

16.  I  pay  i55|  for  a  boy's  suit.     Find  the  cost  of  4  such 
suits. 

17.  3  baskets  of  cherries  cost  25  cents.     How  much  will 
12  baskets  cost  ? 

Suggestion.  —  12  baskets  will  cost  how  many  times  the  cost  of  3 
baskets  ? 


1.    Find  6 

H 

6 

xli. 

Written  Work 

This  means  that  6  x  |  is 

to  be  added  to  6  x  1. 

?  =  6xJ 

6 

6x 

i  =  S 

or  3 ;  6x1  =  6 

;  and  3  +  6  =  9. 

9 

Find  the  value  of 

, 

2.     8  X  41 

11. 

10x2f 

20.  125xl8f 

3.   10x41 

12. 

12x3| 

21.     72  X  24| 

4.     9  X  2f 

13. 

20x5f 

22.   100x14^0 

5.   12x3f 

14. 

45  X  12^ 

23.   132  X  5^\ 

6.    11  X  3^ 

15. 

120  X  22| 

24.   168xl0^\ 

7.   14x22 

16. 

154  X llf 

25.      20  X  18| 

8.   12x8i 

17. 

96  X  6f 

26.      90  X  15| 

9.     6  X  81 

18. 

144  X  91 

27.      50  X  16J 

10.     5  X  3f 

19. 

80x41" 

28.   200  X  15^ 

214  FIFTH  YEAR 

29.  A  book  dealer  purchases  125  books  at  wholesale  at 
f  1 J  each.     Find  the  cost. 

30.  The  car  fare  from  Pittsburg  to  Chicago  on  the  Ft. 
Wayne  is  $10 J.  Find  the  amount  received  from  the  sale  of 
50  tickets. 

31.  A  newsdealer  buys  300  papers  at  1|  cents  each  and 
sells  them  at  2  cents  each.     Find  the  cost  and  the  gain. 

32.  A  huckster  buys  20  dozen  bananas  at  10  cents  per  dozen 
and  sells  them  at  the  rate  of  2  cents  each.     Find  his  gain. 

33.  A  fruit  dealer  buys  a  barrel  of  apples  for  $4|^.  The 
barrel  contains  240  apples.  He  sells  one  half  of  them  at 
the  rate  of  2  for  5  cents  and  the  remainder  at  the  rate  of 
3  for  5  cents.     Find  his  profit. 

34.  A  merchant  buys  a  roll  of  calico  containing  40  yards 
at  5|  cents  per  yard.     Find  the  cost. 

35.  The  merchant  retails  the  calico  at  7|  cents  per  yard. 
Find  the  amount  received  for  the  roll. 

36.  A  boy  lives  If  miles  from  his  school  and  attends  150 
days  in  the  term.  How  many  miles  does  he  walk  in  a  term 
both  to  and  from  school  ? 

37.  A  department  store  employs  100  cash  girls  at  f  2|  per 
week  and  120  other  clerks  at  $4|  per  week.  Find  the 
amount  paid  to  all. 

38.  If  a  man  can  cut  an  average  of  2 J  cords  of  wood  in  a 
day,  how  many  cords  can  he  cut  in  44  days  ? 

39.  A  dealer  in  feed  finds  that  a  car  load  of  600  bushels 
of  oats,  after  paying  freight,  damage,  etc.,  costs  42 J  cents 
per  bushel.     Find  the  cost. 

40.  A  contractor  buys  20  thousand  feet  of  lumber  at 
$20|  per  thousand  and  16  thousand  bricks  at  il6^  per 
thousand.     Find  his  bill. 


FKACTIONS  215 

41.  Find  the  cost  of  24,000  railroad  ties  at  62|  ^  each. 

42.  When  lead  pencils  are  selling  at  $1|  per  gross  (144), 
find  the  cost  of  3550  gross. 

43.  Find  the  cost  of  sewing  buttons  on  72  suits,  at  1|^  a 
suit. 

44.  A  contractor  averages  6|  rd.  a  day  in  digging  a  sewer. 
How  long  is  the  sewer  if  it  takes  him  39  days  to  dig  it  ? 

45.  A  rural  mail  carrier  travels  23J  miles  for  each  delivery. 
Find  the  number  of  miles  traveled  in  310  deliveries. 

46.  An  ocean  steamer  burns  on  an  average  201^^  tons  of 
coal  in  a  day.  How  much  coal  will  it  consume  in  a  voyage 
of  7  days  ? 

Multiplying  an  integer  by  a  mixed  number. 

Analyze  these  problems : 

1.  Multiply  12  by  6| ;  10  by  7|. 

2.  7 1  times  8  hours  are  how  many  hours? 

3.  How  much  do  2|  pounds  of  candy  cost  at  40  cents 
a  pound? 

4.  I  bought  4J  yards  of   ribbon   at   40  cents    a    yard. 
How  much  did  it  cost? 

5.  A  boy  walks  3  miles  in  an  hour.     How  far  can  he 
walk  at  the  same  rate  in  2f  hours  ? 

6.  James  is  6  years  old.     His  mother  is  4|  times  as  old. 
How  old  is  she? 

7.  How  much  will  10|  pounds  of  meat  cost  at  16  cents  a 
pound? 

8.  A  man  bought  7J  gallons  of   oil  at  12^   a  gallon. 
How  much  did  he  pay  for  it? 


216  FIFTH   YEAR 

9.    When  gas  costs  25  cents  per  thousand  feet,  what  is 
my  bill  for  10|  thousand  feet? 

10.  If  a  lot  cost  $200  and  a  house  6|-  times  as  much,  how 
much  did  the  house  cost? 

11.  A  man  worked  20|  days  in  a  month  for  $2  a  day. 
How  much  did  he  earn? 

12.  How  many  inches  equal  9|  feet? 

13.  At  60  cents  a  bushel,  how  much  will  2J  bushels  of 
wheat  cost? 

14.  I  bought  Ij  dozen  collars  at  $2  per  dozen.     How 
much  did  they  cost? 

15.  At  12  cents  a  pound,  how  much  will  15|  pounds  of 
raisins  cost? 

16.  How  much  will  5|  bu.  raspberries  cost  at  $2  a  bushel  ? 

17.  If  a  plumber  is  paid  75  cents  per  hour,  how  much  does 
he  receive  in  3|  hours? 

18.  How  far  will  an  automobile  travel  in  2|  hours  if  it 
travels  18  miles  in  one  hour  ? 

19.  If  the  freight  from  New  York  to  Albany  on  a  ton  of 
merchandise  is  33  cents,  how  much  will  it  be  on  5^^^  tons? 

20.  A  gallon  of  water  weighs  8  pounds.     How  much  do 
10|  gallons  weigh? 

Written  Work 
1.    Multiply  12  by  181. 
12 

181 

2  =  1  X  12  18|  times  12  means  that  I  of  12  is  to  be  added 

9^        ^  to  18  X  12.     i  of  12  =  2,  whicii  added  to  18  x  12 

12  =218. 

218 


FRACTIONS  217 

2.    Multiply  12  by  14|. 


12 


8  =  f  of  12 
48 
12 

176 

14f  times  12  means 
to  14  X  12.    1  of  12  = 
=  176. 

that  f  of  12  is  to  be  added 
:  8,  which  added  to  14  x  12 

Find  products  : 

3,    71  X  6 

17. 

2O2V  X  100 

31. 

116f  X  54 

4.    151  X  9 

18. 

42^L  X  55 

32. 

112^  X  50 

5.    271  X  12 

19. 

64J^  X  39 

33. 

88f  X  28 

6.    120  J  X.  40 

20. 

72J^  X  42 

34. 

30|  X  160 

7.    216^0  X  50 

21. 

102Jg  X  80 

35. 

19^2  X  24 

8.    731  X  15 

22. 

124^^  X  120 

36. 

3,^x60 

9.    1401  X  28 

23. 

12f  X  9 

37. 

145^^  X  55 

10.    100^0  X  60 

24. 

14|  X  10 

38. 

48f  X  84 

:ii.    95-1  X  45 

25. 

20|  X  12 

39. 

21f  X  16 

12.    811  X  21 

26. 

35f  X  18 

40. 

40|  X  25 

13.    1201  X  81 

27. 

951  X  42 

41. 

121f  X  49 

14.    1441  X  108 

28. 

lOOf  X  20 

42. 

lOf  X  18 

15.    150^V  X  60 

29. 

1241  X  120 

43. 

14J  X  24 

16.    180^8  X  18 

30. 

65|  X  32 

44. 

20^2  X  84 

45.    If  the  rate  of  sailing  of  a  vessel  is  18  miles  an  hour, 


how  far  will  it  sail  in  24 J  hours  ? 


46.  Find  the  cost  of  12^  tons  of  coal  at  $6  a  ton. 

47.  Find  the  cost  of  16|  yards  of  silk  at  11.50  a  yard. 

48.  A  farmer  sold  5J  acres  of  land  at  $  40  an  acre.     How 
much  did  he  receive  for  it  ? 


218  FIFTH  YEAR 

49.  If  ribbon  is  sold  at  24  cents  a  yard,  how  much  will  7| 
yards  cost  ? 

50.  At  16  cents  a  pound,  how  much  will  10|^  pounds  of 

cheese  cost  ? 

51.  If  clover  seed  is  selling  at  i  8  a  bushel,  how  much  will 
11|  bushels  cost  ? 

52.  Find  the  cost  of  5J  yards  of  point  lace  at  $  24  a 
yard. 

53.  When  hay  is  selling  for  812  a  ton,  how  much  must  I 
pay  for  16|  tons  ? 

54.  If  a  boy  walks  18  miles  in  a  day,  how  far  can  he  walk 
in  36|  days  ? 

55.  Mr.  Penrose  sold  his  farm  containing  85|  acres  at  $  56 
an  acre.     How  much  did  he  receive  for  it  ? 

56.  Find  the  cost  of  15|  yards  of  velvet  at  $  5  a  yard. 

Multiplying  a  fraction  by  a  fraction. 

1.  What  is  J  of  6  feet  ?   |  of  6  feet  ? 

2.  What  is  1^  of  6  sevenths  ?   f  of  f  ? 

3.  J  of  1^  means  that  we  are  to  take  ^  of  6  equal  parts  of 
a  unit  that  has  been  divided  into  7  equal  parts. 

4.  ^  of  1^  =  how  many  sevenths  ? 

5.  J  of  1^  =  |,  and  I"  of  f  =  2  times  f ,  or  ^. 

Find: 

6.  loff  9.    f  off  12.    f  oflf 

7.  J  of  I  10.    foff  13.    I  of  If 

8.  i  of  I  11.     f  of  f  14.     I   of  fl 


FRACTIONS  219 

15.  What  is  I  of  f?  1  of  1  =  1,  and  I  of  f=  2  times  i 

or  f  . 

16.  •  Observe  that  |  of  |  =  ?  ^  |  =  f 5,  or  |. 

0X0 

Written  Work 

1.    Find  I  of  f     This  means  |  x  f  =  Jf 
Find  products : 


2. 

|x| 

6. 

fxA 

10. 

fxt 

3. 

f  x| 

7. 

f  X  ^ 

11. 

ftx| 

4. 

fx|- 

8. 

|xf 

12. 

fxf 

5. 

fxf 

9. 

ix| 

13. 

fX^TT 

14.  Find  H  X  1|.     Change  to  improper  fractions.     Thus, 
llxl|  =  |x^  =  ^,or2|. 

15.  If  X  21  19.  IJ  X  21  23.  6J  X  9| 

16.  U  X  2f  20.  3|  X  11  24.  121  X  4J 

17.  31x11  21.  4fx7i  25.  10fx3^ 

18.  41x21  22.  9|xl2l  26.  121x121 

27.  Find  the  cost  of  3 J  quarts  of  milk  at  7J^  per  quart. 

28.  A  lady  bought  18 1  yards  of  gingham  at  8|y  per  yard. 
Find  the  cost. 

29.  When  copper  is  selling  at  16|^  per  pound,  find  the 
cost  of  8|  pounds. 

REVIEW 

1.  Find  the  cost  of  2  dozen  cans  of  tomatoes  at  8^  cents 
per  can. 

2.  How  much  does  a  motorman  earn  in  13J  hours  at  22^ 
per  hour  ? 


220  FIFTH   YEAR 

3.  When  copper  is  selling  at  16|  cents  per  pound,  find 
the  cost  of  36  pounds. 

4.  If  platinum  is  selling  at  l|19|  per  ounce,  find  the  cost 
of  7  ounces. 

5.  Find  the  cost  of  21  tons  of  anthracite  coal  at  f  6|  per 
ton. 

6.  A  load  of  soft  coal  contains  50  bushels.     How  much  is 
it  worth  at  7|  ^  per  bushel  ? 

7.  When  apples  are  selling  at  $.64  a  bushel,  find  the  cost 
of  12|  bushels. 

8.  At  8|  cents  per  pound,  how  much  is  the  express- 
age  on  a  package  weighing  48  pounds  ? 

9.  If  a  bale  of  cotton  weighs  475|  pounds,  how  much  is 
it  worth  at  8  cents  per  pound  ? 

10.  How  much  will  17J  quarts  of  ice  cream  cost  at 
20  cents  per  quart  ? 

11.  When  hay  is  selling  at  88|  per  ton,  find  the  cost  of 
34|  tons. 

12.  From  a  piece  of  carpet  containing  61  yd.,  19|  yd.  were 
sold  at  70^  a  yard,  17 J  yd.  at  65^  a  yard,  and  the  remainder 
at  65  ^  a  yard.     For  how  much  was  the  whole  piece  sold  ? 

13.  If  the  above  piece  of  carpet  cost  45  ^  a  yard,  find  the 
entire  gain. 

14.  Find  the  weight  of  14  bags  of  coffee  if  each  bag 
weighs  47|  pounds. 

15.  At  8|  miles  per  hour,  how  far  does  a  steamboat  travel 
in  16  hours  ? 

16.  The  rate  in  example  15  is  the  rate  downstream.  Up- 
stream the  rate  is  2|  miles  per  hour  less.  How  far  would 
the  boat  travel  upstream  in  24  hours  ? 


FRACTIONS  221 


CANCELLATION 


1.     Find  |-  of  ^.  In  changing  y^^  to  |  both  terms  of  the  frac- 

divide 
2x3 


2  V  3  _    6     r»v  2       tion  are  divided  by  3.     Hence,  in  finding  the 

3  ^  5  ~  15'  ^^   5 


2  X  $       2  value  of  - — -  the  work  may  be  shortened  by 

— L_  :3s  _  O  y,  O 

p  X  O       5  rejecting  the  factor  3  from  both  dividend  and 

divisor,  as  indicated  in  the  second  model. 

Cancellation  is   the  process  of   shortening  operations  by 
striking  out  equal  factors  from  both  dividend  and  divisor. 
Cancel  equal  factors  from  both  dividend  and  divisor  when 

5 

possible  ;   thus,  |  x  71  x  3  =  |  x  ^  x  |  =  ^  =  15. 

p       f       1       1 

2.  I  X  2f  X  2  9.  51  X  21  X  4 

3.  If  x4|  xli  10.  I  of  I  X  61 

4.  4  X  21  X  11  11.  J  X  8  X  12f 

5.  J  X  3  X  41  12.  ^%  of  3|  X  10 

6.  3  X  I  of  I  13.  51  X  2^2_  X  31 

7.  51  X  31  x4  14.  5  x3i  X  3| 

8.  61  X  8  X  2f  15.  161  X  41  X  3 

16.  At  8|  cents  per  pound,  how  much  is  the  expressage  on 
a  package  weighing  64  pounds  ? 

17.  At  $9|  a  pair  find  the  cost  of  15  pairs  of  lace  cur- 
tains. 

18.  At  the  rate  of  33 1  miles  an  hour  how  far  will  a  train 
travel  in  10|  hours  ? 

19.  If  a  load  of  coal  weighs  5|  tons,  find  the  cost  at  $6| 
per  ton. 

20.  Where  hay  is  selling  at  S12|  per  ton,  find  the  cost  of 
6^  tons. 


222 


FIFTH   YEAR 


DIVISION   OF   FRACTIONS 


'/z 

l'^'/z=2 


Dividing  a  whole  number  by  a  fraction. 

1.  How    maDj   halves    are    there    in    this 
square  ? 

2.  How  many  times  is  \  contained  in  1  ? 

3.  How  many  times  is  %\  contained  in  f  1? 

in  $2?  insB4? 

4.  What  is  the  quotient  of  tivo  halves 
divided  by  one  half?  of  f  h-  |- ?  What  is  the 
quotient  oifour  halves  divided  by  two  halves  ? 

of  4.  ^   2  9    f)f   6   ^   2  ') 
Ui.   2     •     2   •     ^2     •     2   • 

5.  How  many  fourths  are  there  in  this 
square  ?  What,  then,  is  the  quotient  of  1 
divided  by  J  ? 

6.  How  many  I J  are  there  in  $1  ?    in  $3  ? 

7.  What  is  the  quotient  of  four  fourths  divided  by  one 
fourth?  of  |-5-:f?  What  is  the  difference  between  the 
quotients  of  l-^\  and  |-i?  of  2 -- J  and  f-i?  of  3-^J 
and -152.^  J? 


'A 

1^/4  =  4 


8.    Explain  how  1-i- 1  =  1  H-^;     2-i-J  =  |H-J;     3 -s- 


¥^i;|- 

^i 

=  ll 

-^A;  1- 

■-\  = 

li-/5- 

Give  quotients: 

9.    2^1 

15. 

5- 

-l 

21. 

12-J 

27. 

15-1 

10.    4-i-l 

16. 

6- 

-\ 

22. 

10^1 

28. 

2-i 

11.    5.:- J 

17. 

6- 

-* 

23. 

9^1 

29. 

4-^i 

12.    2^1 

18. 

8- 

-i 

24. 

6^i 

30. 

5^i 

13.    4^1 

19. 

5- 

-i 

25. 

12^* 

31. 

16 -f- 1- 

14.    3^1 

20. 

4- 

-I 

26. 

4-J 

32. 

lO^i 

FRACTIONS  223 

33.  Change  1,  2,  8,  4,  5,  6,  7,  8,  9, 10  each  to  4ths  ;  to  6ths  ; 
to  8ths  ;   to  lOths.      Thus,  1  =  |  =  |  =  f  =  ^. 

34.  What  change  must  be  made  in  ^  and  |  before  they  can 
be  added  or  their  difference  taken  ? 

35.  What  change  did  we  make  in  the  problem  1  -?- 1  before 
we  divided  1  by  ^  ? 

36.  What  change  did  we  make  in  the  fractions  in  exam- 
ple 8  before  one  fraction  was  divided  by  another  fraction? 
This  is  the  first  step. 

37.  When  the  fractions  have  been  made  similar  what  is 
the  second  step  in  dividing  the  fractions  ?  the  third  step  ? 

An7/  number  may  he  divided  by  a  fraction  hy  changing  both 
numbers  to  similar  fractions  and  then  dividing  the  numerators. 


Thus, 

8^ 

l  =  ¥*4=*o^ 

h  4  =  10. 

i^ 

i  =  H-'-A  =  i5H 

-8=    IJ. 

38.   Give 

quotients  : 

4      .    1 

S      .    1 

20  _t.  1 

■5^5 

liJ^¥ 

jr~7 

8^i 

i%^i 

i*^f 

j\-^i 

M^i 

H-i 

fj^i 

M-i 

1^^^ 

ii^l 

iJ-i 

f-^A 

il^i 

il-i 

1^1% 

39.    Give 

quotients  : 

4--i 

1^* 

i^i 

6^1 

ii^l 

i^^i 

2^f 

U^l 

i-i 

li^l 

M-i 

i-i 

if^i 

-J!-f 

f^l 

12^1 

l-A 

i%^l 

M-f 


-H 

-A 

J- 

-1^ 

iV^ 

-A 

J-^ 

■A 

|-^^2 

1- 

^i 

i- 

^f 

i- 

^+ 

!• 

^i 

^' 

^iV 

if 

-^1 

224 


FIFTH   YEAR 


Dividing  a  whole  number  or  a  mixed  number  by  a  fraction. 

An  improper  fraction  is  a  fraction  whose  numerator  is  equal 
to  or  greater  than  its  denominator;  as,  |,  |,  |,  J. 

A  proper  fraction  is  a  fraction  whose  numerator  is  less 
than  its  denominator;  as,  |,  |,  |. 

Change  4J,  5J,  2|-,  51,  7J,  to  improper  fractions. 


1.    Divide  41  by  |. 

4    =  c.  d. 

1^1  = 


¥--- 


6 


Written  Work 


Change  4|  to  the  improper  fraction  f . 
Change  f   and    |  to    similar   fractions. 


Divide 
2.      6 


4 


2i 


21-1 


H 


8. 

9. 
10. 
11. 
12. 
13. 


1|^ 

10     -4- 


12 


12  _^ 
-^3     • 


1 


3i 

4 
5 


14. 
15. 
16. 
17. 
18. 
19. 


i 


21 


6 


-  f 


20.  How  much  are  eggs  per  dozen  when  36  cents  are  paid 
for  2^  dozen  ? 

21.  A  man's  wages  amounted  to  46  dollars  for  9J  days' 
work.     How  much  did  he  receive  per  day  ? 

22.  A  piece  of  ribbon  containing  10  yards  is  cut  into 
badges  each  |^  of  a  yard  in  length.  How  many  badges  can 
be  cut  from  the  piece  ? 

23.  A  merchant  sold  81  cents'  worth  of  ribbon.  If  he 
sold  6 J  yards,  what  was  the  price  per  yard  ? 


8. 

m^H 

14. 

H  - 

-9| 

9. 

14f^2f 

IS. 

8|-   - 

-8^ 

10. 

^^^ 

16. 

8f   - 

-6f 

11. 

6f^4i 

17. 

9|   - 

-H 

12. 

H^H- 

18. 

s-^- 

^2| 

13. 

H^n 

19. 

H  - 

-^1 

FRACTIONS  225 

Dividing  a  mixed  number  by  a  mixed  number. 
Written  Work 

1.  Divide  IJ  by  14  First  change  the  mixed  numbers 

^  _       1  to  improper  fractions,  then  make  the 

— — — '- — •*  fractions  similar,  and  divide  the  nu- 

^^2  "^  ^^  merator  of  the  dividend  by  the  nu- 

I  -H    I  =  9  -f-  8, 1  or  1^   merator  of  the  divisor. 

2.  71^21 

3.  6|^1| 

4.  5|H-lf 

5.  8|  +  2i 

6.  7J-^1| 

7      31-^^1 
/.     03    .    -2 

20.  At  2|  dollars  each,  how  many  vests  can  be  bought 
for  142  ? 

21.  At  $1^  apiece,  how  many  pictures  can  be  bought  for 
$10|  ? 

22.  I  paid  1 28 1  for  cloth  at  f  1|  a  yard.     How  many 
yards  did  I  buy  ? 

23.  I  spent  |17f  for  molasses  at  f  lyg-  a  gallon.     How 
many  gallons  did  I  buy  ? 

24.  At  $1^  each,  how  many  straw  hats  can  be  bought  for 
|14f  ? 

25.  A  merchant  purchases  $50^  worth  of  gas  lamps  at 
84^  a  piece.     Find  the  number  purchased. 

26.  When  3|  bushels  of  apples  cost  $2|,  how  much  will 
one  bushel  cost? 

27.  A  man  earns  $  16 1  in  5 J  days.    How  much  is  this  per 
day? 

28.  At  $2^  per  pair,  how  many  pairs  of  shoes  can  be  bought 
for  $11 1? 


226  FIFTH  YEAR 

Dividing  any  number  by  a  fraction  by  inverting  the  terms 
of  the  divisor. 

1.  How  many  times  is  ^  inch  contained  in  1  inch?  ^  yard 
in  1  yard?  ^  foot  in  1  foot?     Draw  figures  to  illustrate. 

When  the  fraction  |-  is  changed  to  |,  the  fraction  is  said  to 
be  inverted.  It  then  shows  how  many  times  the  fraction  is 
contained  in  1. 

2.  1^1= 1-^1= 1-1= 


3.  1^1  = 1^1  = .  1^1= 

Observe  that  in  each  of  the  above  problems  the  quotient 
equals  1  x   the  fraction  inverted. 

Thus :  1  -  §  =  1  X  2,  or  2  ;  1  --  i  =1  x  f,  or  4. 

4.  Since  1  -f-  i  =  1  x  f ,  or  2,  then  1  -^  |  =  1  x  |,  or  2. 

How  many  times  is  |  contained  in  1?  |?  -f^?  |?  f  ?  |? 

The  number  of  times  each  of  the  above  fractions  is  con- 
tained in  1  equals  the  number  of  times  the  numerator  of 
each  fraction  is  contained  in  its  denominator. 

Find  quotients  by  inverting  the  divisor  and  multiplying: 
Thus:  3-|  =  3xf=  V  =  3!. 


5. 

l^i 

12. 

2-1 

19. 

8-1 

26. 

15^1 

6. 

1-1 

13. 

B-f 

20. 

16-f 

27. 

16-1 

7. 

1-1 

14. 

4-1- 

21. 

24-1 

28. 

12-1 

8. 

1-1 

15. 

5-f 

22. 

20-f 

29. 

8-f. 

9. 

1-1 

16. 

6-^J 

23. 

15-f 

30. 

7-i\ 

10. 

1-f 

17. 

9-fo 

24. 

30-1 

31. 

6-1 

11. 

1-f 

18. 

10-1 

25. 

12-f 

32. 

9-i 

FRACTIONS  227 

Written  Work 
1.    Divide  128  by -If. 

o  Since  l^  is  contained  in  1,  f  |  times, 

^^R  ^—  =  n^  X  —  =  200     ^3  i^  contained  in  128, 128  x  f  |,  or  200 
"      *    25  ;^  times. 

Ani/  number  may  he  divided  by  a  fraction  hy  inverting  the 
terms  of  the  divisor  and  multiplying. 

Divide  : 

2.  18  by  I                        9.    63  by  J  16.    288  by  ^4. 

3.  25  by  I                       10.     72  by  I  17.    400  by  J^- 

4.  28by^                      11.    84by|i  18.   285  by  J^^. 

5.  21byf                      12.    90  by  If  19.    546  by  |l 

6.  36  by  ^9^                    13,    108  by  If  20.    425  by -fl 

7.  42byfi                    14.     84  by  ^2  21.    378  by  || 

8.  54byf                      15.     96byf  22.    324  by  ^^^ 

23.    Divide  36  by  3|. 

Suggestion.  —  Change  the  divisor  to  an  improper  fraction. 

Divide: 

24.  27by2i        30.  84by4J  36.  780  by  7| 

25.  33by3f        31.  75by2f  37.  355  by  8 1 

26.  44  by  4|        32.  90  by  3|  38.  295  by  6| 

27.  60by3f        33.  92  by  2^3^  39.  748  by  3| 

28.  76by4f        34.  85  by  1 1  40.  549  by  8f 

29.  60by6f        35.  245by5f  41.  620  by  7|' 

Divide  : 

42.  Ilfby3f       45.  4-^5  by  If^  48.  10fby2f 

43.  6|byl|       46.  7t^2byl|  49.  15|by2i 

44.  10|  by  2^2-      47.  7f  by  2f  50.  12|  by  o| 


228  FIFTH   YEAR 

MISCELLANEOUS   PROBLEMS 

Divide : 

1.  SJybySf     5.  9fTby8|      9.  27f  by  8^ 

2.  9f  by  4f      6.  65f  by  3f     10.  48i  by  IQi- 

3.  16^by6|  7.    4fby6i  11.    Wf  by  U 

4.  ai^byWJj        8.    14Jby5t  12.    29f^  by  21| 

Problem  12  may  be  expressed  in  this  way  ^'^^  -,  but  it  is 
solved  in  the  same  way.  ^ 

Solve: 

13.  ^  19.     "  ^  ^^  25.     ^  ^  -^'^ 
If 

14.  1^  20.     "'-^  ::  "^  26. 


23- 

3f 

2x 
5}x 

5t- 

^ 

3|-x 
8|  X 

6|-- 

21 

_  95 

101 

15.  ^  21.      '1':  ~'^  27. 

2  X  21 

16.  -— -^  22.     ^V^^^  28. 

17.  ^i_^  23.      ^4 --3  29. 

18.  MjhI  24.     ^Qx^i 

21  8i  31x2 

31.  Mr.  Ames  sold  630|-  pounds  of  wool  at  32i  ^  per  pound. 
How  much  did  he  receive  for  it  ? 

32.  A  farmer  cut  3J  tons  of  hay  per  acre  from  13J  acres. 
Find  the  value  of  the  hay  at  S 1 2|  per  ton. 

33.  Mr.  Anderson  sold  |-  of  66^  acres  of  land  at  f  47|-  per 
acre.     For  how  much  did  he  sell  the  land  ? 

34.  How  many  badges  6|  inclies  long  can  be  cut  from  23|- 
yards  of  ribbon  ? 


I 


FRACTIONS  229 

35.  I  of  I  of  Mr.  Adams's  farm  was  32  acres.  If  he  sold 
the  farm  at  >j)105  per  acre,  how  much  did  he  get  from  the 
sale  ? 

36.  How  many  ribbons  |  of  a  yard  long  can  be  cut  from 
46|  yards  of  ribbon  ? 

37.  Two  boys  buy  a  sled.  One  pays  for  |  of  the  cost  and 
the  other  ^  of  the  cost.  If  the  boy  that  paid  |  of  the  cost 
paid  90^,  how  much  did  the  sled  cost? 

38.  If  any  two  factors  in  a  division  are  given,  how  may  we 
obtain  the  third  factor  ?     Make  problems  to  illustrate. 

39.  The  dividend  is  163|,  the  quotient  is  2181.  Find  the 
divisor. 

40.  IJ  is  the  product  of  6  and  what  other  number  ? 

41.  I  of  the  length  of  a  flag  pole  is  60  feet.  What  is  the 
length  of  I  of  the  pole  ? 

42.  I  of  I  of  the  time  I  worked  for  Mr.  Ward  is  12  days. 
Find  my  pay  for  the  whole  time  at  f  2.50  per  day. 

43.  The  length  of  a  certain  city  square  is  338 1  feet.  Find 
its  length  in  rods. 

44.  An  automobile  ran  Q^^^  miles  in  2|  hours.  Find  the 
average  rate  per  hour. 

45.  James  weighs  160|  lb.,  Sara  108Jg  lb.,  John  135|  lb., 
Mary  121|  lb.,  and  Henry  121|  lb.  Find  |  of  their  com- 
bined weight. 

46.  Paul  averages  2|-  feet  at  a  step.  How  many  steps 
does  he  take  in  going  1  mile  ? 

47.  The  lead  lining  in  a  tank  weighs  3|  pounds  to  the 
square  foot.  How  many  pounds  will  be  necessary  to  line 
a  tank  containing  275J  square  feet  of  inside  surface  ? 


230  FIFTH  YEAR 

COMPARISON  — WHOLE  NUMBERS  AND  FRACTIONS 

1.  1  =  J  ;  I  =  |.     Then  how  do  J  and  |  compare? 

2.  If  a  unit  is  first  divided  into  halves  and  then  each 
half  into  halves,  into  how  many  parts  is  the  unit  divided  ? 
Is  ^  of  a  unit  larger  or  smaller  than  J  of  a  unit  ? 

3.  Divide  a  unit  into  halves,  fourths,  eighths,  and  six- 
teenths, and  show  how  many  sixteenths  of  a  unit  it  takes  to 
make  ^  of  the  unit  ;  J  of  the  unit  ;  J  of  the  unit  ;  ^  of  the 
unit. 

4.  Draw  equal  squares  to  show  that  J  =  |  or  ^^g-. 

5.  Compare  |  and  |  ;  |  and  ^- ;  |  and  f. 

6.  How  does  I  of  20  compare  with  J  of  20  ?  J  of  16 
with  I  of  16  ?   I  of  50  with  ^  of  20  ? 

7.  A  has  40  acres  of  land,  and  B  60  acres.  How  does  A's 
farm  compare  in  size  with  B's  ? 

8.  8  is  what  part  of  12,  16,  24,  32,  48,  72? 

Suggestion. — Make  8  the  numerator  in  each  case  and  the  other 
numbers  the  denominators  and  reduce  the  fractions  to  their  lowest  terms. 
Thus,  y\  =  1;  j\  =  ^;  .«?  =  h  etc. 

9.  If  5  quarts  of  milk  cost  45  cents,  how  much  will  10 
quarts  cost  ?   15  quarts  ?   20  quarts  ? 

10.  Elizabeth  buys  3J  yards  of  ribbon  for  35  cents.  At 
the  same  rate,  how  much  would  she  pay  for  10 J  yards  ? 

Suggestion.  —  How  many  times  3^  is  10^  ? 

11.  A  woodsman  cuts  15  cords  of  wood  in  6  days.  How 
many  cords,  at  the  same  rate,  could  he  cut  in  48  days  ? 

12.  Compare  8  and  2  ;   6  and  4  ;  2  and  8  ;  5  and  10. 

13.  Compare  J  and  ^  ;  ^  and  J  ;  J  and  -^^. 

14.  Compare  24  with  4,  6,  8,  48,  72,  16,  20. 


I 


FRACTIONS  231 


15.  Draw  a  square  inch  and  show  that  |  of  it  =  ^  of  it; 
that  ^  of  it  =  Y^g  of  it. 

16.  If  I  of  a  man's  weekly  wages  is  12.75,  how  much  is 
J  of  his  weekly  wages  ? 

Suggestion.  —  I  is  how  many  times  \7 

17.  3|  pounds  of  rice  cost  35  cents.     At  that  rate  how 
much  will  7  pounds  cost  ? 

18.  If  |-  of  my  money  is  f  10,  and  George  has  6  times  my 
money,  how  much  has  George  ? 

19.  In  New  York  9J  inches  of  rain  fell  in  3  months.     At 
that  rate  how  much  will  fall  in  a  year  ? 

20.  If  a  man  pays  13675  for  60  acres  of  land,  at  the  same 
rate  how  much  should  he  pay  for  120  acres  ? 

21.  My  telephone  bill  is  112.85  a  month.     At  that  rate 
how  much  should  I  pay  in  2|  years  ? 

22.  My  coal  bill  for  5|-  tons  is  811.     What  is  the  bill  of 
my  neighbor  who  buys  27  J  tons  at  the  same  rate  ? 

23.  If  30  bushels  of  oats  sell  for  113.20,  how  much  will  60 
bushels  sell  for  ? 

24.  If  a   boy  receives  $7.50  for   two  weeks'  work,  how 
much  should  he  receive  for  12  weeks'  work? 

25.  How  much  will  a  clerk  earn  in  a  year  if  he  earns  flSO 
in  3  months? 

26.  If  4  tons  of  coal  cost  $8|,  how  much  will  16  tons  cost  ? 

27.  When  5  books  cost  117.50,  how  much  will  25  such 
books  cost  ? 

28.  A  man  walked  11|  miles   in   3  hours.     At   the  same 
rate,  how  far  would  he  walk  in  6  hours  ? 


232  FIFTH  YEAR 

REVIEW  OF  FRACTIONS 

1.  A  boy  earns  |2|  a  week  and  spends  |1|.  If  he  puts 
the  remainder  in  bank,  what  will  his  bank  account  be  in 
19  weeks  ? 

2.  May  went  to  the  store  with  120.  If  she  spends  |2| 
for  a  pair  of  shoes  and  $4|  for  a  hat,  how  much  change  will  she 
receive  ? 

3.  From  a  web  of  muslin  containing  60  yards,  19|  yd. 
were  sold  to  one  customer,  13J  yd.  to  another,  and  9^  yd. 
to  another.      How  many  yards  remained  ? 

4.  A  dealer  sold  2  loads  of  coal  at  17.20  a  ton.  If  the 
first  load  contained  2|  T.,  and  the  second  d^  T.,  how  much 
did  he  receive  ? 

5.  How  many  yards  of  muslin  can  be  bought  for  75^, 
if  3  yards  cost  25^? 

6.  If  John  weighs  96|  lb.  and  Mary  weighs  361  lb.  less 
than  John,  how  much  do  they  both  weigh  ? 

7.  A  farmer  bought  480  acres  of  land.  He  sold  148J 
acres  to  one  man,  and  125-|  acres  to  another.  What  was  the 
remainder  worth  at  f'20  an  acre? 

8.  How  many  days  will  it  take  a  man  to  earn  $126|,  if 
he  earns  1 2|  a  day  ? 

9.  A  man  dies  leaving  14440.  He  leaves  J^  ^f  it  to  his 
son,  J  of  it  to  his  daughter,  |  of  it  to  his  widow,  and  the  rest 
to  a  hospital.     How  much  does  each  receive  ? 

10.  John  bought  3  pieces  of  cloth  containing  19 J  yd.,  26^ 
yd.,  and  35|  yd.  respectively.     How  many  yards  did  he  buy? 

11.  A  man  worked  43|  hr.  one  week,  and  36^^  hr.  the 
next.     How  many  hours  did  he  work  in  the  two  weeks  ? 


I 


FRACTIONS  233 


12.  A  man  paid  ^  of  his  indebtedness  one  year,  J  of  the 
remainder  the  second  year,  and  J  of  what  then  remained  the 
third  year.  Then  he  owed  $  516.  How  much  did  he  owe  at 
first  ? 

13.  From  a  certain  number  2|  +  3 J  was  subtracted,  leav- 
ing a  remainder  of  lO^^^^.     What  was  the  number  ? 

14.  One  fifth  of  a  certain  number,  minus  2|,  equals  87|-. 
What  is  the  number  ? 

15.  Mrs.  Smith  bought  4  pieces  of  lace  containing  4|  yd., 
6|  yd.,  5 J  yd.,  and  9 J  yd.,  respectively.  How  much  were 
they  worth  at  12|  ^  a  yard? 

16.  If  an  acre  of  land  is  worth  f  32,  how  much  is  |  of  an 
acre  worth? 

17.  A  man  paid  f  45  for  |  of  a  quantity  of  grain.  Find 
the  value  of  the  entire  quantity  at  the  same  rate. 

18.  How  many  poor  families  can  be  supplied  with  |^  of  a 
ton  of  coal  each  from  9  J  tons  ? 

19.  Find  the  cost  of  36 J  pounds  of  tea  at  32^  a  pound. 

20.  If  I  of  a  yard  of  silk  cost  45  cents,  what  is  the  value 
of  6|  yards  at  the  same  rate  ? 

21.  What  number  taken  from  the  sum  of  16 J  and  28f  will 
leave  19J  ? 

22.  What  is  the  cost  of  |  of  a  yard  of  muslin  at  12^  a  half 
yard  ? 

23.  The  sum  of  two  numbers  is  126|,  and  the  larger 
number  is  94|.     What  is  the  smaller  number  ? 

24.  A  man  spends  i6J  for  board,  812|  for  clothing,  $3^ 
for  books,  and  has  $12  left.  How  many  dollars  and  cents 
had  he  at  first  ? 


234  FIFTH  YEAR 

25.  If  75)^  is  the  cost  of  |  of  a  yard  of  cloth,  what  is  the 
cost  of  5  yards  ? 

26.  il.50  is  the  value  of  |  of  a  yard  of  broadcloth.  How 
many  yards  can  be  bought  for  $20  ? 

27.  I  of  a  number  is  9.     What  is  the  number  ? 

28.  In  traveling  72  miles  a  man  went  |  of  the  distance 
the  first  day,  ^  of  the  distance  the  second  day,  and  the  re- 
mainder the  third  day.  How  far  did  he  travel  the  third 
day? 

29.  From  a  farm  of  225|  acres  there  were  sold  150^  acres. 
How  many  acres  were  left? 

30.  How  much  must  be  paid  for  16  tables  at  $7J  each? 

31.  At  $f  each,  how  many  books  can  I  buy  for  $36  ? 

32.  A  man  bought  a  hat  for  f  5|,  a  pair  of  shoes  for  i6-|-, 
a  pair  of  gloves  for  13 J,  and  a  suit  for  $22^.  How  much  did 
he  pay  for  all  ? 

33.  A  clerk  earns  $75  a  month  and  spends  i36|.  How 
much  has  he  left? 

34.  At  $.87 J  a  bushel,  what  is  the  cost  of  56  bushels  of 
grain  ? 

35.  How  many  chairs,  at  $5J  each,  can  be  bought  for 
$2621? 

36.  A  lady  bought  |  of  a  yard  of  narrow  lace.  If  yards  of 
medium  width  lace,  and  2J  yards  of  wide  lace.  How  many 
yards  did  she  buy  in  all  ? 

37.  From  a  piece  of  muslin  containing  40  yards  there  were 
sold  25 1  yards.     How  many  yards  remained? 

38.  At  $.12^  a  yard,  what  is  the  cost  of  42  yd.  of  muslin? 

39.  How  many  pencils,  at  ^^  each,  can  be  bought  for 
$1.16? 


FRACTIONS  235 

40.  One  coat  requires  2|-  yards.  How  many  coats  can  be 
made  out  of  S5^  yards? 

41.  Jolm  weighs  124|^  pounds,  and  Ned  weighs  18|  pounds 
less.     How  many  pounds  does  Ned  weigh? 

42.  A  farmer  sold  35|  bushels  at  one  time,  and  21 J 
bushels  at  another  time.     How  many  bushels  did  he  sell? 

43.  A  tailor  uses  9|  yards  of  cloth  for  a  suit.  How  many 
yards  will  it  take  for  32  suits? 

44.  John  and  James  cut  3|  cords  of  wood  in  one  day.  In 
how  many  days  can  they  cut  84:|  cords? 

45.  A  man  raised  236J  bushels  of  oats,  and  sold  129| 
bushels.     How  many  bushels  had  he  left? 

46.  A  man  exchanged  with  a  grocer  2^  bushels  of  pota- 
toes at  60^  a  bushel,  for  6|  pounds  of  bacon.  How  much  did 
the  grocer  charge  per  pound  for  the  bacon  ? 

47.  A  merchant  sold  some  grain  for  $63  which  was  J  of 
its  cost.     What  was  the  cost  of  the  grain? 

48.  I  of  a  building  is  valued  at  $300?  What  is  the  value 
of  the  whole  building? 

49.  11  lb.  of  butter  cost  30^.     Find  the  cost  of  2f  lb.  ' 

50.  A  owns  160  sheep  and  B  owns  ^  as  many  as  A. 
C  owns  J  as  many  as  B.     How  many  sheep  do  all  own  ? 

51.  Show  that  multiplying  or  dividing  both  terms  of  a 
fraction  by  the  same  number  does  not  change  its  value. 

52.  How  many  potatoes  are  there  in  12  barrels,  if  one 
barrel  contains  2  bushels  3  pecks? 

53.  48-121  =  ?     12|-5f  =  ?     10f-l|  =  ? 

54.  For  5  cents  one  can  buy  3  oranges.  How  much  must 
be  paid  for  12  oranges? 


DECIMALS 

Decimal  parts  of  the  dollar. 

1.  How  many  dimes  equal  a  dol- 
lar? Then  what  part  of  a  dollar  is 
a  dime? 

2.  How  many  cents  equal  a  dol- 
lar ?     Then  what  part  of  a  dollar  is  a  cent  ? 

3.  Ten  mills  equal  one  cent.  How  many  mills  equal  a 
dollar?     Then  what  part  of  a  dollar  is  a  mill? 

Mills  are  not  coined,  but  are  used  for  exactness  in  computations. 

When  we  think  of  a  dollar  as  dimes,  it  has  10  equal  parts ; 
when  we  think  of  a  dollar  as  cents,  it  has  100  equal  parts ; 
when  we  think  of  a  dollar  as  mills,  it  has  1000  equal  parts. 
A  mill  is  yl(j  of  a  cent ;  a  cent  3^  of  a  dime  ;  and  a  dime  J-^y  of 
a  dollar. 

This  division  of  the  dollar  into  tenths,  hundredths,  thou- 
sandths, etc.,  we  call  decimal  parts  of  the  dollar. 

The  decimal  point  is  the  point  separating  dollars  and  cents. 
Thus,  in  $2.75  the  point  separates  2  dollars  from  75  cents. 

4.  What  decimal  part  of  a  dollar  are  5  dimes?  6  dimes? 

8  dimes?  9  dimes? 

5.  What  decimal  part  of  a  dollar  are  5  cents?  8  cents? 

9  cents?  10  cents? 

236 


DECIMALS  237 

The  first  place  to  the  right  of  the  decimal  point  is  occupied 
by  dimes  or  tenths  of  a  dollar ;  the  second  place,  by  cents  or 
hundredths  of  a  dollar;  the  third  place,  by  mills  or  thour 
sandths  of  a  dollar. 

Thus,  8  dimes,  5  cents  =  85  cents.  Cents  occupy  the  first  two  places 
to  the  right  of  the  decimal  point.  Observe  that  dimes,  cents,  and  mills 
can  always  be  written  as  decimal  parts  of  a  dollar ;  thus,  8  dimes  =  f  .80 ; 
2  mills  =  $  .002. 

6.  In  $1,256,  state  what  each  figure  represents. 

7.  Name  the  parts  of  a  dollar,  first  as  tenths,  hundredths, 
and  thousandths;  then  as  cents  and  mills:  $.65,  $S.05, 
$2,005,  $.50,  $.75,  $.80,  $.705. 

8.  Write  in  figures :  six  dollars,  five  cents ;  ten  dollars, 
fifty  cents  ;  three  mills  ;  five  cents ;  five  mills. 

We  may  also  find  tenths,  hundredths,  thousandths,  etc.,  of 
any  unit. 

READING  AND  WRITING  DECIMALS 

One  tenth  inay  be  written  .1  as  well  as  -^-^  ;  one  hundredth 
may  be  written  .01  as  well  as  ^^^  ;  and  one  thousandth  may 
be  written  .001  as  well  as  y^Vo- 

1.  Read:  .8  ft.,  .5  lb.,  .7  pk.,  .5  ft.,  .7  mi. 

A  decimal  point  is  a  period  placed  before  tenths. 

A  decimal  fraction  is  any  number  of  lOths,  lOOths,  lOOOths, 
etc.,  of  a  unit.  When  expressed  after  a  decimal  point  and 
without  a  written  denominator  it  is  usually  called  a  decimal. 

The  first  place  to  the  right  of  the  decimal  point  is  called 
tenths,  the  second  place  hundredths,  and  the  third  place  thou- 
sandths. 

2.  In  55.55,  the  5  hundredths  is  what  part  of  the  5  tenths  ? 
the  5  tenths  is  what  part  of  the  5  units?     the  5  units  is 

.  what  part  of  the  5  tens? 


238  FIFTH  YEAR 

In  any  number,  whether  a  whole  number  or  a  decimal,  the 
"Value  of  a  figure  in  any  place  is  -^^  of  the  value  of  the  same 
figure  standing  one  place  to  the  left. 

3.    What  is  the  largest  decimal  division  of  a  unit?     the 
second  largest  ?    the  third  largest  ? 


4. 

.06  =  y|^  =  10^ 

7. 

•^  — TO  —  TOO  —  TTFTT-O" 

5. 

•-^  =  Tto  =  loVo 

8. 

.025-  ^(^00   -  100(5-(F 

6. 

•^5=  ito  =ToVo 

9. 

.349  =  ^0^0  =ToW 

Observe  that  a  decimal  is  always  less  than  a  unit. 


tC     H     O     P     H     W     H 

5   2   5-256 

This  number  is  read,  five  hundred  twenty-five  and  two  hun- 
dred fifty-six  thousandths. 

10.  What  do  we  call  the  decimal  point  when  we  read  a 
number?  What  word,  then,  always  joins  the  whole  number 
and  the  decimal  ? 

Observe  that  we  express  every  number  as  units,  or  ones,  and  parts  of  a 
unit.     Thus :  525.256  is  525  units  and  .256  of  a  unit. 

As  the  first  decimal  division  of  a  unit  is  tenths,  we  always 
begin  to  enumerate  the  decimal  at  tenths'  place ;  thus : 
tenths         hundredths         thousandths 
.0  0  5 

11.  At  what  place  do  we  begin  to  enumerate  whole  numbers  ? 

12.  Read  the  following:  .25,  .025,  25.005,  7.05,  321.1, 
0.875,  1.008,  100.001,  0.001. 

13.  Write  as  decimals:  -f^,  ^J^,  ^ff^,  J^,  ^-^f^,  j-^2_^, 
26-1^^,  lOO^J^O'  1t!^'  703-V^. 


DECIMALS  2S9' 

Write  decimally : 

14.  Two  thousandths. 

15.  Two  and  two  thousandths. 

16.  Five  hundredths. 

17.  Two  hundred  and  two  thousandths. 

18.  Two  hundred  two  thousandths. 

19.  Three  and  five  tenths. 

20.  Seventy-five  hundredths. 

21.  Five  hundred  and  five  thousandths. 

22.  Thirty-three  thousandths. 

23.  Ninety-five  thousandths. 

24.  Two  hundred  and  five  hundredths. 

25.  Six  and  nine  tenths. 

26.  Six  hundred  and  six  hundredths. 

COMPARISON  OF   COMMON  FRACTIONS  AND   DECIMALS 

1-   t^-tVo  =  AVo;  .5  =  .50  =  .500. 

2.  Do  naughts  at  the  right  of  a  decimal  affect  its  value? 
Annexing  naughts  to  the  right  of  a  decimal  does  not  affect  its 

value, 

3.  What  is  a  fractional  unit? 

4.  What  is  the  largest  fractional  unit  that  may  be  ex- 
pressed decimally?  the  second  largest?  the  third  largest? 

5.  Change  -f^-^  to  tenths. 

6.  Express  .25,  .45,  .75,  .025,  each  in  the  form  of  a  com- 
mon fraction. 

7.  Change  .5  to  equivalent  decimals  expressed  in  hun- 
dredths and  thousandths.     Thus,  .5  =  .50  =  .500. 


240  FIFTH  YEAR 

8.  Name  the  three  largest  fractional  units  in  their  order; 
the  three  largest  decimal  fractional  units. 

9.  Change  y^  to  an  equivalent  decimal. 

Changing  a  decimal  to  a  common  fraction. 

1.  Change  .75  to  a  common  fraction  in  its  lowest  terms. 

Expressed  in  the  form    of  a    common    fraction 
^75  =  r^Q  =  1      .75  =  j^5(j.     By  dividing  both  numerator  and  denomi- 
nator of  r^  by  25,  we  reduce  it  to  its  lowest  terms,  |. 

To  change  a  decimal  to  a  common  fraction,  write  the  decimal, 
omitti7ig  the  decimal  point,  place  the  decimal  denominator  be- 
neath it,  and  change  the  fraction  to  its  lowest  terms. 

Change  to  fractions : 

2.  .15  4.    .9  6.    .75  8.    .125 

3.  .825  5.    .325  7.    .025  9.    .425 

10.    Memorize  the  following  equivalents  : 

J=.5or.50  1  =  .2  or  .20  |  =  .8or.80 


.      i  =  .25 

1= 

.4  or  .40 

i= 

.125 

|  =  .75 

1= 

.6  or  .60 

f= 

.375 

11.    Change 

to  tenths :  ^ 

;  i; 

I;  I;  t- 

12.    Express  as  decimal  hundredths  :  J  ;  f ; 

i;f. 

Change  to  fractions  and  reduce  to  lowest  terms : 

13.    .45 

19.    .20 

25.     .40 

31. 

.075 

14.    .625 

20.    .60 

26.     .48 

32. 

.025 

15.    .75 

21.    .125 

27.     .150 

33. 

.12 

16.    .65 

22.     .90 

28.     .50 

34. 

.225 

17.    .375 

23.     .96 

29.    .025 

35. 

.700 

18.    .80 

24.     .72 

30.    .08 

36. 

.800 

DECIMALS  241 

ADDITION   OF   DECIMALS 

1.  What  kind  of  fractions  can  be  added  or  subtracted? 

In  adding  or  subtracting  decimals,  like  units  must  always 
be  written  under  one  another;  thus,  .8+  .85  +  .096  may  be 
written  thus:  .8  .8-f    .8  =  1.6 

Added  .85  Test:  .05 +  .09=    .14 

.096  .006=   .006 

T7f46  1.746 

2.  In  how  many  of  the  decimals  are  there  tenths  to  be 
added?  hundredths?  thousandths? 

3.  Why  must  tenths  be  written  under  tenths,  hundredths 
under  hundredths,  etc.  ? 

A  mixed  decimal  is  a  whole  number  and  a  decimal  united  j 
thus,  4  +  .05,  or  4.05,  is  a  mixed  decimal. 

Written  Work 

1.    Add  45.5 +  6.005 +  40. 
45.5 

6.005  Keep  the  decimal  points  and  units  of  the  same  order  in  a 

^Q  column,  and  add  as  in  whole  numbers,  placing  the  decimal 

Q-j   rr.r      poiut  in  the  sum  under  the  points  above. 

Find  the  sums  of  the  following : 

2.  .1  +  . 2 +  .35 +  .365  =  ? 

3.  .02 +  .05 +  .095 +  .056  =  ? 

4.  .05 +.007 +  .089 +.11  =  ? 

5.  1.2  +  3.4  +  4.5  =  ? 

6.  3.04  +  4.05  +  6.099  =  ? 

7.  .005 +  .007 +  .009 +  .0101  =  ? 

8.  2.006  +  7.009  +  9.012  =  ? 

9.  .001 +  .001 +  .0902  =  ? 


242 

FIFTH 

YEAR 

, 

10. 

10  +  2.1  +  14.9  +  17.85  =  ? 

11. 

.9 +  .85 +  .005 +  .25 +  .895  = 

:? 

Add: 

12.    1.45 

13.    .424 

14.        .7 

15. 

11.111 

3.7 

8.2 

.425 

3.06 

10.01 

6.16 

18.54 

.635 

2.005 

19.009 

7.011  • 

.000 

16.    18.002 

17.    .040 

18.    89.400 

19. 

.707 

2.056 

48.010 

75.800 

101.101 

121.114 

.708 

761.612 

96.086 

2,02 

89.010 

1245.000 

27.409 

20.  Find  the  sum  of  15.38,  9.17,  3.07,  and  20.35. 

21.  A  boy  picked  on  Monday,  .75  of  a  bushel  of  berries  ; 
on  Tuesday,  .875  of  a  bushel;  on  Wednesday,  1.125  of  a 
bushel.     How  many  bushels  did  he  pick  in  the  three  days  ? 

22.  Helen  paid  $.25  for  a  handkerchief,  $2.75  for  a  pair 
•of  shoes,  S.45  for  lace,  and  ff  1.49  for  a  waist.  How  much 
•did  they  all  cost  ? 

23.  A  train  runs  the  first  hour  19.625  miles  ;  the  second 
hour,  20.5  miles  ;  the  third  hour,  20.75  miles  ;  the  fourth 
hour,  21.225  miles.  How  far  does  it  run  in  the  four 
hours  ? 

24.  Find  the  number  of  pounds  in  the  following  purchases  : 
1.25  lb.  of  cheese,  3.5  lb.  of  sugar,  .5  lb.  of  cloves. 

25.  The  distance  from  Harrington  to  Houston  is  4.31 
miles,  thence  to  EUendale  11.25  miles,  thence  to  George- 
town 8.37  miles.  How  far  is  it  from  Harrington  to 
^Georgetown  ? 


DECIMALS  24a 


SUBTRACTION  OF  DECIMALS 
Find  differences : 


1. 

.5".3  =  ? 

5.    .008 -.002  =  ? 

2. 

.9-. 8-=? 

6.    .014 -.011  =  ? 

3. 

15.8-11.7  =  ? 

7.    .08 +  .09 -.12 +  .04 +.02  =  ? 

4. 

4.7-3.2  =  ? 

8.    .009 +  .003 -.007 -.004  =  ? 

Written  Work 
1.    From  16.35  subtract  11.76. 

■*^"*"^  Keep  the  decimal  points  in  a  column  and  sub* 

11.76  tract  as  in  whole   numbers,  placing  the  decimal 

4.59  point  in  the  difference  under  the  points  above. 

2.        7.  3.     16.  4.       1.101        5.    265.36 

1.21  3.046  .796  84.468. 

6.      25.2  7.    151.003  8.    954.1  9.     36.291 

9.18  78.076  258.375  17.456. 

10.    144.001        11.    300.  12.      86.59        13.    728.3 

12.256  261.385  53.594  619.333: 


14.  Warren  had  17.50  and  spent  13.75.  How  much  had 
he  remaining  ? 

15.  The  distance  between  two  towns  is  9  miles.  After 
I  have  walked  3.625  miles,  how  far  have  I  yet  to  walk  ? 

16.  A  man  having  120  acres  of  land,  sold  to  one  man 
28.75  acres,  and  to  another,  35.5  acres.  How  many  g,cres 
had  he  left  ? 

17.  If  I  pay  i  1.25  for  car  fare,  |.65  for  dinner,  and  |.90 
for  an  umbrella,  how  much  change  have  I  left  from  a  five- 
dollar  bill  ? 


2U  FIFTH   YEAR 

18.  The  second  floor  of  a  house  is  18.78  feet  above  the 
floor  of  the  celhir,  and  the  first  floor  is  7.92  feet  above  it. 
How  far  is  it  from  the  first  floor  to  the  second? 

19.  Four  lots  measure  in  width  128.08  ft.  Three  of  them 
are  respectively  25  ft.,  32.72  ft.,  and  36.9  ft.  wide^  What  is 
the  width  of  the  fourth  ? 

20.  A  boy  having  84.25  spent  for  skates  81.25,  for  a  caj 
f  .50,  and  for  a  hockey  stick  $.45.     How  much  had  he  leff^ 

21.  A  lady  having  25.75  pounds  of  butter  sold  to  one; 
customer  3.25  pounds,  to  another  8.5  pounds,  to  another 
7.25  pounds,  and  the  balance  to  a  fourth  customer.  Hc^. 
many  pounds  did  the  fourth  customer  buy? 

22.  From  a  ham  weighing  18.125  lb.  a  butcher  sold  3.25  lb., 
4.501b.,  2.75  lb.,  and  2.5  lb.     How  many  pounds  had  he  left  ? 

23.  A  fisherman  brought  home  four  trout  weighing  respec- 
tively 1.25  pounds,  .875  pounds,  1.375  pounds,  and  1.125 
pounds.     How  much  less  than  5  pounds  did  they  all  weigh? 

24.  A  farmer  cut  40  tons  of  hay  in  1905.  He  sold  6.85 
tons  to  one  man,  and  5.55  tons  to  another.  He  fed  the  rest 
to  his  stock.     How  many  tons  did  he  feed  to  his  stock? 

25.  A  lady  bought  4.75  yards  of  woolen  cloth,  11.625 
yards  of  cotton  cloth,  and  6.875  yards  of  silk.  How  many 
yards  less  than  30  yards  did  she  buy  ? 

26.  A  man  having  120  spent  14.75  for  board,  $2.80  for 
a  room,  f  .88  for  laundry,  $1.75  for  a  pair  of  gloves,  and  $3.50 
for  a  pair  of  shoes.     How  much  had  he  left? 

27.  A  merchant  purchased  the  following:  coffee  $15.25, 
sugar  $18.35,  cakes  $11.65,  fruit  $27.75,  canned  corn  $8.45, 
canned  peaches  $12.30,  and  vegetables  $21.90.  How  much 
less  than  $  120  was  the  amount  of  his  bill? 


DECIMALS  245 

MULTIPLICATION  OF  DECIMALS 

Multiplying  a  decimal  by  an  integer. 

1.  0  X  .3  means  that  .3  is  taken  as  an  addend  6  times. 
Thus,  .3  -h  .3  +  .3  -f  .3  +  .3  =  15  tenths  or  1.5. 

By  multiplication  5  x  .3  =  1.5. 

2.  5  X  .03  means  that  .03  is  taken  as  an  addend  5  times. 
Thus,  .03  +  .03  +  .03  +  .03  +  .03  =  15  hundredths  or  .15. 

By  multiplication  5  x  .03  =  .15. 

3.  5x1.007  means  that  1.007  is  taken  as  an  addend  5 
times.    Thus,  1.007  4- 1.007+1.007  +  1.007  +  1.007  =  5.035. 

By  multiplication  5  x  1.007  =  5.035. 

4.  In  each  problem  above,  how  many  decimal  places  are 
there  in  the  multiplicand  ?  how  many  in  the  product  ? 

Observe  that  in  multiplying  a  decimal  by  an  integer^  the 
product  contains  the  same  number  of  decimal  places  as  the 
multiplicand. 

Written  Work 
1.    Multiply  5.75  by  6. 

6x5  hundredths  =  30  hundredths,  or  3  tenths  and 

5.75  no  hundredths.     Write  naught  in  hundredths'  place 

g  and  carry  the   3   tenths.      6x7   tenths  =  42  tenths ; 

-  42   tenths  +  3   tenths  =  45   tenths,  or   4  units  and  5 

tenths.      Write    5   in    tenths'  place   and  carry  the  4 

units.      Place   the  decimal    point.      6x5  units  =  30 

units;  30  units  +  4  units  =  34  units. 

Find  products  : 

2.  8  X  .015   6.  7  X  .97  10.  86  x  .861  14.  55  x  .066 

3.  9  X  .005   7.  12  X  .025  ii.  74  x  .037  15.  39  x  .467 

4.  8  X  .17    8.  6  X  .604  12.  67  x  .92  '  16.  48  x  .095 

5.  11  X  .207   9.  9  X  .054   13.  44  x  .705   17.  36  x  .081 


246  FIFTH   YEAR 

18.  How  mucli  will  7  arithmetics  cost  at  1.82  apiece? 

19.  At  $  .35  apiece,  how  much  will  24  chickens  cost  ? 

20.  A  rod  is  16.5  feet.     How  many  feet  are  there  in  9  rods  ? 

21.  When  a  man  earns  f  3.65  per  day,  how  much  does  he 
earn  in  26  days  ? 

22.  A  pound  of  cream  cheese  costs  $  .115.  How  much  do 
126  pounds  cost  ? 

23.  If  an  automobile  averages  17.75  miles  an  hour,  how  far 
will  it  travel  in  14  hours  ? 

Multiplying  a  decimal  by  a  decimal. 

1.  Multiply  1.5  by  4.  When  a  decimal  is  multiplied  by 
an  integer,  what  do  you  observe  about  the  number  of  decimal 
places  in  the  product  ? 

2.  Multiply  .1  by  .01  ;  ^^  x  i^o  =  loViT  =  -^^l-  ^Mti- 
ply  1.5  by  .5;  1.5=  if;  ii  X -^%=^\=  .lb.  When  a 
decimal  is  multiplied  by  a  decimal,  what  do  you  observe 
about  the  number  of  decimal  places  in  the  product  ? 

Written  Work 

1.    Multiply  .75  by  .3. 

Since  there  are  two  decimal  places  in  the  multiplicand  and  1  in  the 
multiplier,  point  off  3  decimal  places  in  the  product,  making  the  answer 
.225. 

•  ^^  Test :     .75  =  xVo,   and  .3  =  ^.    ^o\  x  ^  =  iWu 

»3  or  .225,  a  decimal. 

^225 

Multiply  as  in  integers^  pointing  off  as  many  decimal  places 
in  the  product  as  there  are  decimal  places  in  both  factors. 


1 

IT 

DECIMALS 

2 

Find  products  : 

2. 

.8X.27 

8. 

7.24  X  8 

14. 

.025x124 

3. 

.5X.45 

9. 

.011  X  42 

15. 

22.5  X  4.04 

4. 

.15  X. 256 

10. 

.57X.15 

16. 

.75  X  .624 

5. 

6.5x10 

11. 

2.03  X  .4 

17. 

1.44  X  5.5 

6. 

5.7x9.4 

12. 

.145x48 

18. 

2.4  X  64 

7. 

3.21x4.5 

13. 

11.4  X  150 

19. 

1.33  X  44 

24T 


20.  Find  the  cost  of  11.5  yards  of  cloth  at  12|^  cents  a 
yard. 

21.  Mrs.  Crane  bought  3.5  pounds  of  steak  at  f  .16  per 
pound,  6  pounds  of  sugar  at  f  .05  per  pound,  4  pounds 
of  coffee  at  i  .28  per  pound,  and  3  quarts  of  cranberries  at 
$.10  per  quart.  She  gave  in  payment  3  one-dollar  bills. 
How  much  change  should  she  receive  ? 

22.  How  much  will  41.25  yards  of  linoleum  cost  at  $1.25 
per  yard  ? 

23.  A  train  between  Los  Angeles  and  San  Francisco  runs 
13.5  hours  at  the  rate  of  35.7  miles  per  hour?  What  is  the 
distance  between  the  two  cities  ? 

24.  A  mail  carrier  averages  3.25  miles  per  hour  while  de- 
livering mail.  If  lie  spends  5.25  hours  delivering  each  day 
how  far  does  he  walk  per  day  ? 

25.  Find  the  cost  of  5.125  yards  of  silk  at  $1.75  a  yard. 
At  the  same  price  per  yard  find  the  cost  of  8.875  yards. 

26.  At  $2.50  per  day,  how  much  will  4  men  earn  in  6.5 
days  ? 

27.  A  cubic  foot  of  water  weighs  62.5  pounds.  How 
much  do  12.75  cubic  feet  of  water  weigh  ? 


248  FIFTH   YEAR 

DIVISION  OF  DECIMALS 
Dividing  a  decimal  by  an  integer. 

Written  Work 

4')  84 

1.  Divide  .84  by  4  in  this  way  :      ^^^ 

Divide  and  test,  placing  a  decimal  point  in  the  quotient 
before  beginning  to  divide: 

2.  6)M  5.   7). 714  8.   7). 847 

3.  3). 96  6.   5). 535  9.   6). 936 

4.  8). 808  7.   4). 848  10.   8). 896 

11.    Explain  why  adding  naughts  to  the  right  of  a  decimal 
does  not  change  its  value  ;  thus,  .8  =  .80,  .05  =  .050. 

It  is  sometimes  necessary  to  add  naughts  to  the  right  of 
the  dividend  to  complete  the  division. 


12.   Divide  .12 

by^ 

5.     5).12  =  5).120 
.024 

Find  the  quotients 

and  test : 

13.  4). 3 

14. 

8). 6              15. 

61 

^ 

16.    5). 28 

17.       .6^2 

25.    .024^    6 

33. 

.108^    3 

18.       .9-3 

26.   .102-    3 

34. 

.08 -^    2 

19.     .12-6 

27.   .039^13 

35. 

.125^    5 

20.   .005 -r- 5 

28.    .144-12 

36. 

.16^   4 

21.   .008-^4 

29.   .015-^    3 

37. 

.35-^    7 

22.     .27  -^  9 

30.   .063-^    7 

38. 

.077 -h  11 

23.        .2-4 

31.   .904^   8 

39. 

.022-    2 

24.     .24-8 

32.     .72-10 

40. 

.036 -f-    6 

DECIMALS  249 

Dividing  a  mixed  decimal  by  an  integer. 

Written  Work 

Divide  in  this  way : 

1.   6)6.648  2.   8)24.600  3.   9)729.83 

1.108  3.075  81.09| 

Observe  that  in  dividing  a  decimal  or  a  mixed  decimal  by 
an  integer,  the  dividend  is  simply  separated  or  partitioned 
into  equal  parts. 

4.   Divide  39.25  by  25.  5.   Divide  12.648  by  24. 


1.57 

.527 
)12.648 
12  0 
64 

48 

168 

168 

25)39.25     24; 
25 
14.2 
12.5 

1.75 

1.75 

How  many  times  is  25  contained 
in  39?  in  14.2?  in  1.75? 

In  practice,  we  simply  divide  as 
in  the  division  of  integers.  Since 
24  is  larger  than  12.648,  the  quo- 
tient must  be  a  decimal. 

Place  a  decimal  point  directly  above  or  below  the  decimal 
point  in  the  dividend,  before  beginning  to  divide;  then  divide 
as  in  the  division  of  integers. 

Divide  and  test : 

6.    69.92 --23 

14. 

.945 --35             22.     8.437^59 

7.    29.54 --14 

15. 

60.32-52             23.    233.32-38 

8.    195.2-32 

16. 

.968^44             24.    283.88-^47 

9.    401.4-18 

17. 

.828-5-23             25.      6.497-^73 

10.    3.434-34 

18. 

5.18^37             26.    16.150^34 

11.    156.4-46 

19. 

.0833 --49             27.    55.660-92 

12.    1.014-26 

20. 

1.566-^54             28.     5.460^84 

13.    5.084^41 

21. 

2.546 -J- 67             29.    1.6272-18 

250  FIFTH   YEAR 

30.    Divide  12  by  16. 
12-^-16  =  12.00^16. 


_^       12  is  equal  to  12.00,  wJiich  divided  by  16 


16)12.00    equals  .75. 

112  ^  decimal  point  must  be  placed  after  an 

oQ   integer  before  naughts  are  annexed. 

80 
Divide : 

31.  20  -i-   75  35.      44  -4-  99  39.  605  by  1210 

32.  60^150  36.  110^220  40.  513  by  2052 

33.  24-^228  37.  340 -f- 1700  41.  208  by  1664 

34.  30  -f-  375  38.  510  -i- 1020  42.  Ill  by  8888 

Dividing  any  number  by  a  decimal. 

1.  In  .5,  .25,  .025  move  the  decimal  point  one  place  to  the 
right  and  read  the  result;  two  places  to  the  right;  three 
places  to  the  right. 

2.  In  what  short  way,  then,  may  a  decimal  be  multiplied 
by  10?  by  100?  by  1000? 

3.  Multiply  each  of  the  following  numbers  first  by  10  and 
read  the  results.     Then  by  100.     Then  by  1000 : 

.2,  2.5,  .25,  .04,  .025,  .002,  .020,  .001,  40.25,  4.05,  200,  21.0, 
.012,  1.001,  10.1,  400.1,  04.04,  50.0,  4.004. 

Explain  why : 

4.  .2).24  =  2)2.4 ;  .04).0164  =  4)1.64 ;  1.6)25.6  =  16)256 

5.  .6)18  =  6)180;    .12)144  =  12)14.4;   .08).48  =  8)48 

6.  .09)8.1  =  9)810;   .25)2.25  =  25)225;       .05)5  =  5)500 
/.    Observe  that  when  both  the  dividend  and  the  divisor 


DECIMALS  251 


of  ^  are  multiplied  by  10,  thus,  i|>^  ^^  =  |,  the  quotient 

remains  the  same. 

8.  Tell  the  number  of  places  the  decimal  point  must 
be  moved  to  the  right  in  both  dividend  and  divisor  in  each 
of  the  following  problems,  in  order  to  make  the  divisor  an 
integer ;  then  give  quotients : 

9.  .5). 25         .2)2.6        4)4.4         .6)66         8)8.08 

10.    .03). 15      .12). 96         .07). 21         .09). 81        .05). 05 

Written  Work 

1.    Divide  .025  by  .0«5.  Make  the  divisor  an  integer  by  moving 

Qc-N  Qoc       5  ^2  5  *^^  decimal  point  two  places  to  the  right 

^ =     '    fv~r       A  in  both  dividend  and  divisor.    Then  solve 

'    '  *  as  in  dividing  a  decimal  by  an  integer. 

A  decimal  is  divided  by  a  decimal  hi/  moving  the  decimal 
point  in  both  dividend  and  divisor  the  number  of  places  to  the 
rif/ht  necessary  to  make  the  divisor  a  whole  number,  and  divid- 
ing as  in  the  division  of  a  decimal  by  an  integer. 
Divide : 

2.538  by  .27  20.  .0095  by  .19 
.5655  by  .65  21.  20.25  by  .45 
.6150  by  .82  22.    6.192  by  .72 

27.93  by  .57  23.    3.360  by  .35 

52.51  by  .59  24.    2.016  by  .72 

6.216  by  .74  25.    826.5  by  .95 

.6225  by  .75  26.    375.2  by  .56 

8.930  by  .94  27.    7.728  by  .84 

440.8  by  .58  28.    8.025  by  .25 


2. 

.325  by  .5 

11. 

3. 

.756  by  .9 

12. 

4. 

6.96  by  .8 

13. 

5. 

.444  by  .6 

14. 

6. 

.888  by  .12 

15. 

7. 

1.445  by  .17 

16. 

8. 

2.695  by  .35 

17. 

9. 

3.528  by  .42 

18. 

10. 

3.034  by  .37 

19. 

252 

FIFTH  YEAR 

Find  quotients : 

29.        .005^5 

39. 

40.098-^1.23. 

30.  .625^.05 

31.  5.55-^5 

1.23)40.098  =  123.)4009.?5 

32.      17.28^.12 

40. 

55.968 -i- 1.32       ' 

33.      3.036^.06 

41. 

97.875^2.61 

34.      3.728-?- .016 

42. 

437.836-5.32 

35.        .864-^.24 

43. 

214.302-3.82 

36.      3.654-^.21 

44. 

46.695-1.65 

37.    10.044 -.36 

45. 

139.956  H- 3.21 

38.      8.007  ^  .03 

46. 

86.784-^2.26 

REVIEW  OF  DECIMALS 

1.  At  f  8.25  per  ton,  how  many  tons  can  be  bought  for 
141.25? 

2.  From  five  hundred  eighty  and  sixty-seven    ten-thou- 
sandths take  ninety-six  and  forty-nine  tliousandths. 

3.  John  has  .75  of  i2  and  spends  .3  of  it.      How  much 
does  he  save  ? 

4.  If  a  car  conductor  earns  f  1.75  a  day,  how  long  will  it 
take  him  to  earn  1638.75? 

5.  If  8.75  tons  of  coal  cost  $44.80,  how  many  tons  can  be 
bought  for  $21.76? 

6.  If  I  paid  1720  for  land  at  $37.50  an  acre,  how  many 
acres  did  I  purchase  ? 

7.  How  many  tons  are  there  in  272^  tons,  15.7  tons,  9^ 
tons,  and  33.5  tons? 

8.  To  the  sum  of  14.5  and  9.7  add  their  difference. 

9.  What  is  the  value  of  7.5  tons  of  hay  at  $18.75  per  ton? 


DECIMALS  253 

10.  The  distance  from  Pittsburg  to  San  Francisco  is 
2747.9  miles,  and  from  Pittsburg  to  Chicago,  507.1  miles. 
How  far  is  it  from  Chicago  to  San  Francisco  ? 

When  possible,  express  the  numbers  in  the  following  deci- 
mally : 

11.  A  girl  sent  27  pieces  to  a  laundry  that  charged  her 
seventy-five  cents  a  dozen  for  washing  and  ironing  them. 
What  was  her  bill  ? 

12.  Mrs.  Rorer  mixed  15.5  lb.  of  fat  with  2.25  lb.  of  potash 
and  made  soap  which  she  cut  into  pieces  weighing  one  eighth 
of  a  pound  each.     How  many  pieces  of  soap  had  she  ? 

13.  The  weight  of  a  diamond  before  it  was  cut  was  3.875 
carats.  After  it  was  cut,  its  weight  was  2.50  carats.  How 
much  was  lost  in  the  cutting  ? 

14.  Each  of  two  pillows  weighs  4.75  pounds,  and  a  bolster 
weighs  7|  pounds.     Find  the  weight  of  all. 

15.  At  $2|^  a  ton,  how  many  tons  of  ice  can  be  bought  for 

$3.75  ? 

16.  If  I  bought  2  gallons  of  gasoline  and  used  .75  of  it  to 
clean  a  dress,  how  many  quarts  did  I  use  ? 

17.  A  merchant  bought  1200  gas  fixtures  at  $.08^  each 
and  sold  them  at  f  .10  each.     How  much  did  he  gain? 

18.  A  24  story  city  building  averages  14.75  ft.  to  a  story. 
How  high  is  the  building  ? 

19.  Find  the  value  of  17,745  bricks  at  17.50  per  M. 

20.  A  merchant  bought  oil  at  89.43  per  barrel.  He  sold 
it  at  8 11.48  a  barrel,  and  gained  -1451.  How  many  barrels 
did  he  have  ? 

21.  Divide  5  pounds  by  .005  of  a  pound. 


PERCENTAGE 

In  Common  Fractions  we  learned  that  a  number  may  be 
divided  into  any  number  of  equal  parts  and  any  number  of 
these  may  be  taken. 

Thus,  f  of  60  means  that  60  is  divided  into  4  equal  parts  and  3  of 
these  parts  are  taken. 

In  Decimal  Fractions  we  learned  that  a  number  may  be 
divided  into  10,  100,  1000,  etc.,  equal  parts,  and  that  any 
number  of  these  parts  may  be  taken. 

Thus,  .9  of  60  means  that  60  is  divided  into  10  equal  parts  and  that  9 
of  these  equal  parts  are  taken. 

We  now  come  to  a  subject  that  divides  a  number  into  100 
equal  parts  only.     We  call  this  subject  Percentage. 

In  common  fractions  we  compute  by  halves^  thirds^  fourths^ 
sixths^  etc. ;  in  decimal  fractions  we  compute  by  tenths,  hun- 
dredths, thousandths,  etc. ;  but  in  percentage  we  compute  by 
hundredths  only. 

Another  name  for  hundredths  is  per  cent,  usually  writ- 
ten "%." 

We  may  now  write  any  number  of  hundredths  in  three 
different  ways,  thus:  j^-q,  .08,  8%  ;  -ff^,  .25,  25%. 

Percentage  is  simply  an  application  of  decimal  fractions. 

1.  Write  the  following  numbers  as  per  cents : 

.05     .03     .15     .20     .25     .40    .06    .75 

2.  Write  the  following  as  decimals: 

5%  20%  7%  15%  25%  16%  18%  24%   50%    75%. 

254 


PERCENTAGE 


255 


3.  Show  by  equivalent  decimals  that  naughts  added  to  the 
riglit  of  a  decimal  do  not  affect  its  value. 

4.  Write  as  decimals,  and  as  per  cents : 

i   f  sV  A  iV  f  I  f 

5.  What  is  the  difference  between  .05  of  $100  and  5%  of 

iioo? 

6.  5  %  =  2V  ^^  ^  number ;  10  %  =-j^  of  a  number. 

7.  25  %  of  $100  may  be  found  in  two  ways  :    (a)  25  %  =  J 
J  of  $100  =  $25.    (5)  25%  =.25;  .25  x  $100  =  $25. 

Learn  the  following  : 


50  %=J 

m%=i 

75  % = f 

331%=  J 

12|%=i 

40  %  =  | 

25  0/0=1 

10  %=tV 

80  %  =  t- 

20  %=i 

5    %  =  2V 

371%  =  ! 

Give  per  cents  at  sight : 

8.  20%  of  $50 

9.  25%  of  $60 

10.  10%  of  $40 

11.  50%  of  $80 

12.  40%  of  $75 

13.  5%  of  $40 

14.  6%  of  $6 

15.  75%  of  $20 

16.  12i%  of  $72 


17.  331%  of  30  days. 

18.  50%  of  60  minutes. 

19.  75%  of  100  books. 

20.  40%  of  20  rods. 

21.  5%  of  40  weeks. 

22.  16|%  of  100  pounds- 

23.  10%  of  70  bushels. 

24.  25%  of  24  hours. 

25.  12-1%  of  800  bushels. 


256  FIFTH   YEAR 

Written  Work 

1.    Find  28%  of  7500  bushels  of  oats. 
7500  bu. 

OQ 

•   "  Since  percentage  is  simply  so  many  hundredths  of 

60000  anything,  28  o/^  of  7500  bushels  equals  .28  of  7500 

15000  bushels,  or  2100  bushels. 
:ilOO#bu. 

Find  : 

2.  27%  of  $395  7.   35%  of  190.60       12.   75%  of  1605 

3.  14%  of  $478  8.   40%  of  $20.50       13.    37%  of  $2005 

4.  24%  of  $527  9.   10%  of  $2004        14.   45%  of  $6745 

5.  6%  of  $57.40     10.     5%  of  $200.60     15.   80%  of  $905 

6.  5%  of  $90.80     11.     7%  of  $500.50     16.    98%  of  $7008 

17.  Mr.  Jordon  bought  a  horse  for  $175  and  sold  it  for 
90%  of  the  cost.     For  how  much  did  he  sell  the  horse  ? 

18.  Raymond  has  $165  in  the  savings  bank  and  Bertha 
has  80  %  as  much.  How  much  more  money  has  Raymond 
in  the  bank  than  Bertha  ? 

19.  The  distance  between  two  cities  is  1080  miles. 
After  45%  of  the  distance  is  traveled,  how  much  of  the 
distance  remains   to  be  traveled? 

20.  Mr.  Watson  earned  $1580  in  a  year,  and  his  son 
Henry  (j5%  as  much.     Find  the  amount  Henry  earned. 


21.    The   salary   of   a  school  teacher  last  year  was 
and  this  year  her  salary  was  increased  25%   of  last  year's 
salary.     Find  her  present  salary. 


PERCENTAGE  257 

22.  Paul  lives  560  rods  from  the  schoolhouse  and  David 
72  %  as  far.  Find  the  number  of  rods  David  lives  from  the 
schoolhouse. 

23.  Mr.  Adams  borrows  $365  for  one  year,  and  pays  6% 
for  the  use  of  the  money  for  the  time.  How  much  money 
will  pay  the  debt  when  due  ? 

24.  Mr.  Brown  has  loaned  11200  to  one  party  and  81600 
to  another  party.  How  much  does  Mr.  Brown  get  each  year 
for  the  use  of  the  money  if  each  party  pays  him  5  %  of  the 
amount  borrowed? 

25.  Find  5%  of  20;  of  40 ;  of  50;  of  60;  of  80. 

26.  A  newsboy  sells  $18  worth  of  papers  and  gets  40% 
for  selling.     How  much  does  he  earn  ? 

27.  Mary  has  $  24  in  the  savings  bank,  and  deposits  25  % 
as  much  as  she  has  in  the  bank.     Find  the  amount  deposited. 

28.  A  boy  borrows  $200  to  go  to  school,  and  pays  the 
lender  5%  for  the  use  of  the  money  for  one  year.  How 
much  does  he  pay  for  its  use  ? 

29.  A  boy  bought  a  pony  and  a  cart.  The  pony  cost  %  80, 
and  the  cart  60  %  as  much  as  the  pony.     Find  the  total  cost. 

30.  A  man  had  400  sheep.  On  Monday  he  sold  25  %  of 
them.  On  Tuesday  he  sold  25  %  of  the  remainder.  How 
many  sheep  had  he  then  ? 

31.  In  a  spelling  test  of  30  words,  James  missed  20%. 
How  many  words  did  he  spell  correctly? 

32.  \  =  y^o  =  ?  %.     Compare  \  and  .20  ;  \  and  20  %. 

33.  A  man  bought  a  house  for  $2800.  He  paid  78%  of 
the  amount  cash,  and  gave  his  note  for  the  balance.  For 
how  much  did  he  give  his  note  ? 

34.  A  merchant  sold  in  one  year  $25,375  worth  of  goods. 
His  profits  were  20  %  of  the  sales.     Find  his  profits. 


258  FIFTH  YEAR 

INTEREST 

1.  Mr.  James  Adams  borrows  $200  from  Mr.  John 
Buchanan  for  2  years  to  send  his  son  to  school,  and  agrees 
to  pay  Mr.  Buchanan  6  %  of  the  money  for  the  use  of  it 
each  year.  How  much  does  it  cost  Mr.  Adams  for  the  use 
of  the  money  the  first  year?  How  much  does  it  cost  Mr. 
Adams  for  the  use  of  the  money  for  the  2  years  ? 

2.  If  Mr.  Adams  settles  with  Mr.  Buchanan  at  the  end  of 
two  years,  how  much  in  all  does  he  give  Mr.  Buchanan  ? 

Interest  is  money  paid  for  the  use  of  money. 

The  principal  is  the  sum  of  money  on  which  the  interest 
is  paid. 

The  rate  of  interest  is  a  certain  number  of  hundredths  of 
the  principal  paid  for  the  use  of  the  principal  for  1  year. 

The  amount  is  the  sura  of  the  principal  and  the  interest. 

In  finding  interest  it  is  always  necessary  to  know  the  time. 
The  interest  for  2  yr.  equals  2  times  the  interest  for  1  yr.  ; 
the  interest  for  6  mo.  equals  J  the  interest  for  1  yr. ;  the 
interest  for  2  mo.  equals  J  the  interest  for  1  yr. 

3.  In  Prob.  1  what  is  the  principal  ?  the  rate  of  inter- 
est ?  the  interest  for  1  yr.  ?  the  interest  for  2  yr.  ?  the 
amount  at  the  end  of  2  yr.  ? 

How  much  is  the  interest  at  6  %  on: 

4.  $  100  for  11  yr.  ?  10.    $  150  for  3  mo.  (J  yr.)  ? 

5.  I  200  for  21  yr.  ?  li.    $  80  for  2  yr.  ? 

•  6.  I  300  for  11  yr.  ?  12.  $  200  for  f  yr.  ? 

7.  $250for6mo.  (lyr.)?  13.  $  100  for  2^  yr.  ? 

8.  $400  for  If  yr.?  14.  $900  for  1|  yr.  ? 

9.  $  800  for  2|  yr  ?  15.  $  750  for  1 1  yr.  ? 


INTEREST 
INTEREST  FOR   YEARS   AND   MONTHS 


259 


1.    What   part  of   a   year   are    6   months?     4   months'* 
3  months  ?    2  months  ?    1  month  ? 


Written  Work 

1.    What  is  the  interest  on  $  200  for  2|-  years  at  6%  ? 
f  200  principal 


.06  rate 


$  12.00  interest  for  one  year 

21 

$  30.00  interest  for  2 J  years 


The  interest  for  1  year  is  .06 
of  the  principal,  or  $  12.  The  in- 
terest for  2|  years  is  2^  x  $  12,  or 
^30. 


Multiply  the  principal  hy  the  rate  and  the  product  hy  the 
number  of  years. 


Find  the  interest  on  ; 

2.  $200  for  1  year  at  5%. 

3.  1 900  for  2  years  at  8%. 

4.  $150  for  3  years  at  6%. 

5.  1 700  for  4  years  at  4  % . 

6.  $150  for  11  years  at  4%. 

7.  $96  for  2  years  at  8%. 


9.  $150  for  41  years  at  5%. 

10.  $  190  for  21  years  at  6  % . 

11.  $  600  for  2 J  years  at  4  % . 

12.  $950 for  9 mo.  at  6%. 

13.  $  940  for  2f  years  at  7  % . 

14.  $650forf  year  at  6%. 

15.  $225for  |year  at  8%. 


8.    $75  for  3|  years  at  7%. 
Find  the  interest  and  amount  at  6  %  of  : 

16.  $200  for  6  months.  19.    $620  for  3  mo. 

17.  $400  for  4  months.  20.    $270  for  8  mo. 

18.  $150  for  2  yr.  2  mo.  21.    $350  for  9  mo. 

22.  Frank  loaned  Mr.  Brown  $250  for  2  years  and  6 
months  at  6  %  interest.  How  much  money  will  it  take  to 
pay  the  loan  ? 


OPERATIONS   WITH   UNITED    STATES   MONEY 


10 

mills  = 

I  cent 

10 

cents  = 

I  dime 

10 

dimes  = 

=  I  dollar 

10 

dollars 

=  I  eagle 

1.  From  tlie  above  table  tell  why  United  States  money  is 
called  a  decimal  system  of  money. 

2.  How  many  cents  equal  a  dollar  ?  What  part  of  a  dol- 
lar is  1  cent  ? 

3.  A  cent  is  what  part  of  a  dime  ?  A  dime  is  what  part 
of  a  dollar  ?     Cents  are  written  as  hundredths  of  a  dollar. 

4.  Read  as  hundredths  of  a  dollar  : 

$0.01     $0.02     10.03     15.07     $9.09    $8.07. 

Note.  —  1  cent  may  be  written  either  $0.01  or  |  .01 ;  25  cents  may  be 
written  either  -10.2.5  or  $.25,  etc.  The  naught  preceding  the  decimal 
point  does  not  affect  the  result,  and  is  sometimes  written  to  show  more 
prominently  that  cents  and  not  dollars  are  represented. 

5.  How  many  mills  equal  $1?  What  part  of  a  dollar 
is  1  mill  ?  Mills  are  written  as  thousandths  of  a  dollar. 
Thus,  1  mill  is  written  $0,001.  $0,005  may  be  read  one 
half  cent.     Why? 

Mills  are  not  coined,  but  are  used  for  convenience  in  computations. 
In  final  results  any  part  of  a  cent  is  usually  regarded  by  the  seller  as 
a  whole  cent.     Thus,  for  a  bill  amounting  to  $0,565,  we  pay  $0.57. 

6.  How  does  moving  a  number  one  place  to  the  right  affect 
its  value?  one  place  to  the  left? 

200 


OPERATIONS   WITH   UNITED   STATES  MONEY       261 

The  rules  for  addition,  subtraction,  multiplication,  and 
division  of  decimals  apply  to  United  States  money  since  it 
is  a  decimal  system. 

Written  Work* 

I.  Find  the  cost  of  27  yards  of  silk  at  S  0.87J  a  yard. 

^^•^^^  Study  of  Problem 

^i~9c  !•   Why  do  we  change  ^^  to  5  mills? 

2.   What  is  the  name  of  the  right-hand  place  in 
'^"^^  the  product  ? 

$  23.625  3.    What  is  the  business  answer  to  this  problem. 

•  Find  the  cost  of  : 

2.  4  yd.  of  lace  @  10.37^.  5.  8  lb.  of  roast  @  llj  ^. 

3.  6  bu.  of  potatoes  @  1 0.62^-.  6.  25  bu.  apples  @  i  \\. 

4.  9  doz.  eggs  @  1 0.12|.  7.  36  cords  of  wood  @  -fSf . 

Find  the  amount  of  : 

8.  23  yd.  of  cloth  @  121  ^.  9.    14  cakes  of  soap  @  21  ^ 
14  boxes  corn  starch  @  8  ^.  37  boxes  macaroni  @12|^. 

31  lb.  of  raisins  @  30  ^.  14  cans  of  soup  @  10  ^. 

10.  At  $  1.50  each,  how  many  readers  can  be  bought  with 
$6.00? 

150^)600)^(4  times  or  readers.  ^^^^°  the  divisor  contains 
^^-.  cents,  both  dividend  and  divisor 
may  be  changed  before  dividing. 

II.  At  il.25  each,  how  many  pairs  of  gloves  can  be 
bought  for  $57.50? 

12.  A  farmer  sold  potatoes  at  2  bushels  for  $  1.50.  He 
received  $  87.50.     How  many  bushels  did  he  sell  ? 

*  For  short  methods  of  performing  operations  of  this  kind,  see  p.  175, 


262 


FIFTH   YEAR 


13.  Walters  &  Company  sold  sleds  at  65  cents  each. 
They  received  $  31.20.     How  many  dozen  sleds  did  tiiey  sell  ? 

14.  Find  the  cost  of  boarding  for  12  weeks  at  17.50  a  week. 

15.  A  merchant  bought  ^  dozen  pairs  of  shoes  at  $2.75 
a  pair.     How  much  was  paid  for  all  ? 

16.  A  bookseller  sold  56  books  at  80.12i  each,  37  books 
at  $0.40  each,  and  75  books  at  10.25  each.  How  much 
money  did  he  receive  for  all  ? 

17.  At  $.02|  each,  how  much  will  1  gross  of  tablets  cost  ? 

18.  A  man  paid  $43.75  for  carpet  at  $1.75  a  yard.  How 
many  yards  did  he  buy  ? 


BILLS 

The  following  is  a  common  form  of  hill. 


1 

Boston,  Mass.,  M.  fO,  1907. 

iVi'Ui/.  fayyv&Qy  B'baw-n, 

38fliiigj^t  0f  Morris  Bros.  &  Co., 

175    BEACON    ST. 

TERMS  :  Cash.                                                            phone  365. 

/O  yd.  ^\Utiyv(f     @  f0.06\ 
fO    "    ^umA           @      0.06-^ 
20    "    €cdUo-          @      0.0  7\ 

f 
/ 

66 
63 

60 

i 

78 

BILLS  263 

Who  sold  the  goods  ?  Who  purchased  the  goods  ?  When 
and  where  was  the  purchase  made  ?  What  words  show  that 
the  bill  has  been  paid  ? 

The  words  "Received  payment,  Morris  Bros.  &  Co.," 
are  called  the  receipt  of  the  bill.  Who  received  the  money  ? 
When  a  clerk  receives  payment  for  a  bill,  he  always  writes 
the  receipt  of  the  firm,  per  his  own  name  or  initials.  The 
receipted  bill  should  be  kept  by  the  buyer  to  show  that  the 
bill  has  been  paid. 

Every  bill  should  show  :  (a)  the  place  and  date  of  purchase; 
(6)  fhe  names  of  the  buyer  and  the  seller;  (<?)  the  quantity^ 
the  price,  and  the  cost  of  each  item,  and  the  amount  of  the 
bill. 

1.  Mrs.  James  Robinson,  on  a  certain  day,  buys  from 
Morris  Bros.  &  Co.,  12  cans  of  Acme  corn  @  ^0.12J,  18 
pounds  sugar  for  $  1.00,  3  pecks  potatoes  @  $0,25. 

Make  out  the  receipted  bill. 

Make  out  receipted  bills  for  the  following  sales,  using  your 
father's  name  as  buyer,  and  the  name  of  your  local  merchant 
as  seller : 

2.  3|- lb.  rice     @  $  0.08.      3.    12  yd.  muslin     @$0.09. 
10  lb.  prunes  @     0.121  lo  yd.  lace  @    0.12J. 

2  bags  salt     @      0.10.  2  pair  socks      @    0.35. 

4.  William  Thomas  bought  of  J.  A.  Crawford  &  Co.,  New 
Castle,  Pa.,  Oct.  10, 1905, 15  lb.  butter  at  28^  per  lb. ;  10  doz. 
eggs  at  24^  per  doz.;  35  lb.  lima  beans  at  11^  per  lb. 
Make  out  receipted  bill,  representing  yourself  as  clerk. 

5.  Mrs.  J.  M.  Rowe  bought  of  Johnston  &  Son,  Buffalo, 
N.Y.,  Dec.  22,  1905,  2  dressed  turkeys  weighing  12J  lb.  and 
13  lb.  respectively,  at  22^  per  lb. ;  5  lb.  of  lamb  chops  at 
Idff  per  lb.     Clerk,  James  Brown. 


264 


FIFTH   YEAR 


6.  W.  M.  Hays  &  Son,  Baltimore,  Md.,  dealers  in  general 
merchandise,  sold  to  Frank  N.  Clark,  Jan.  12,  1905,  the  fol- 
lowing bill  of  goods : 

7|  lb.  butter  @  24/  ;  6  lb.  cheese  @  11 J  /;  14  yd.  calico  @ 
7^/;   1  can  lard,  weighing  8|  lb.,  @  12/. 

Supposing  that  you  are  the  clerk  and  some  neighbor  is  the 
buyer,  make  out  receipted  bills  for  the  following  purchases 
at  your  local  stores  : 

7.  81  lb.  lard  @  lO/;  6  cans  corned  beef  @  15/;  81  lb. 
ham  @  14|/;  8  lb.  sausage  @  12i/. 

8.  3  hassocks  @  98/;  6  chairs  @  f  1.25;  12  yd.  carpet  @ 
$1.10;  2  rockers® -12.90;  1  lamp  @  f  1.65. 

9.  1  saw  @  75/;  3  gas  heaters  @  14.90;  3J  doz.  screws 
@  12/;  lOi  lb.  lawn  seed  @  20/;  8  joints  stove  pipe  @ 
30/;  2  elbows  @  40/. 

Another  form  of  bill  is  commonly  used  when  services  have 
been  rendered,  as  well  as  material  furnished.     For  example  : 


Akron,  Ohio,  June  1,  1907. 
3^a  R.  la.   f(yyvtc.,  h^. 

a  (A.  cAalU               @     0.06 
R.   la.  fa^&a.. 

f9 
/ 

00 
60 
¥■8 

10 

98 

BILLS  265 

The  creditor  is  the  person  who  sells  the  goods  or  does  the 
work. 

The  debtor  is  the  person  who  buys  the  goods  or  for  whom 
the  work  is  done. 

In  the  bill  on  p.  98  Mrs.  Brown  is  debtor  to  Morris  Bros., 
since  she  owes  for  the  goods  purchased,  and  Morris  Bros,  are 
tlie  creditors,  since  they  furnished  the  goods.  In  the  last 
bill  on  p.  264  Mr.  Burroughs  is  the  debtoj'  for  work  received, 
and  Mr.  Jones  is  the  creditor  for  work  he  has  done. 

1.  T.  S.  Ball  owes  Dr.  S.  N.  Pool,  Lloyd  Building,  Pitts- 
burg, Pa.,  for  services  as  follows :  Jan.  1,  1907,  to  1  call,  $2 ; 
Jan.  12,  1907,  to  1  call,  $2;  Jan.  14,  1907,  office,  $1; 
Jan.  16,  1907,  to  1  call,  82.  Make  out  and  receipt  the 
bill  if  paid  Feb.  1,  1907. 

2.  Boydson  &  Co.  owe  Charles  Frampton,  Detroit,  Mich., 
for  services  as  follows : 

March  10,  1907,  6  hr.  delivering  goods  @    f  0.20 

March  11,  1907,  trip  to  country  2.00 

March  12,  1907,     "     "        "  2.00 

March  13,  1907,     "     "        "  2.00 

March  14,  1907,  repairs  to  wagon  3.75 

Write  the  receipted  bill  of  Boydson  &  Co.,  if  paid  April 
1,  1907. 

3.  James  Brown  owes  Stamm  Bros,  for  labor  and  materia] 
as  follows:  June  1,  1907,  189  ft.  lumber  at  8^  per  foot; 
June  4,  1907,  50  lb.  cement  at  4^  per  pound ;  June  8,  1907, 
15  days  labor  at  84.50  per  day. 

Receipt  this  bill  if  paid  July  1,  1907. 


DENOMINATE  NUMBERS 
Liquid  Measures 


A  gallon,  a  quart,  and  a  pint  measure  should  be  brought  into 
Pupils  should  measure,  and  thus  learn  the  relative  capacities. 

Liquid  measures  are  used  iu  measuring  liquids. 


2  pints 

=  1  quart  (qt.) 

4  quarts 

=  1  gallon  (gal.) 

311  gallons 

=  1  barrel  (bbl.) 

63  gallons 

=  1  hogshead  (hhd.) 

1  gallon 

=  231  cubic  inches 

1  gal.  =  4  qt. 

=  8pt.=32gi. 

1.  How  many  pints  equal  a  gallon  ?  a  half  gallon  ? 

2.  How  man}'  quarts  equal  16  pints  ?   24  pints  ?   36  pints  ? 

3.  How  many  gallons  equal  28  quarts  ?    12  qt.  ?    32  qt.  ? 


266 


4  gal.  =  4  X  8  pt. 
2  qt.    =2x2  pt. 
1  pt. 

=  32  pt. 
=   4pt. 
=    1  pt. 

4  gal.  2  qt.  1  pt. 
Change  : 

=  37  pt. 

DENOMINATE  NUMBERS  267 

Written  Work 

1.    Change  4  gal.  2  qt.  1  pt.  to  pints. 

Since  there  are  8  pints  in  1  gal- 
lon, in  4  gallons  there  are  4  times 
8  pints  or  32  pints.  Since  there  are 
2  pints  in  1  quart,  in  2  quarts  there 
are  2  times  2  pints,  or  4  pints.  32 
pints -f  4  pt.  +  1  pt.  =  37  pt.  Hence, 
4  gal.  2  qt.  1  pt.  =  37  pt. 

2.  6  gal.  1  pt.  to  pints.  4.    4  gal.  3  qt.  to  pints. 

3.  8  gal.  1  qt.  1  pt.  to  pints.     5.    5  gal.  2  qt.  1  pt.  to  pints. 

6.  Change  J  gal.  to  pints. 

7.  Mary  bought  S^  gallons  of  cream  at  10^  a  pint.    How 
much  did  it  cost  her  ? 

8.  A  grocer  sold  6^  gallons  of  vinegar  at  8  ^  a  pint.     How 
much  did  he  receive  for  it  ? 

9.  Change  127  pt.  to  gallons,  etc. 

OM  07  f     •    +  Since    2    pints  =  1    quart,     there 

J)1J7,  no.  ot  pints.  ^ill  ^^  ^  ^g  ^^^^  ^^^^^^  ^^  p. ^^^ .  ^j^^^ 

4)63,  no.  of  qt.    -f  1  pt.  is,  63  qt.  +  1  pt.      Since  4  quarts  = 

15,  no.  of  gal.  +  3  qt.  1  gallon,  there   will   be   ^  as  many 

127  pt.  =  15  gal.  3  qt.  1  pt.         ^^^^^""^  ^'  "^""^^^^ '  *^^^  '^  ^^  ^^^'  + 

3  qt. 

Note.  —  The  numbers  in  the  operation  must  be  regarded  as  abstract. 
Do  not  say  127  pints  -^  2  =  63  quarts  -\- 1  pint.  It  is  evident  that  127 
pints  -^  2  would  equal  63^  pints. 

Change  : 

10.  375  pt.  to  quarts,  etc.  14.  469  qt.  to  gallons,  etc. 

11.  846  pt.  to  quarts,  etc.  15.  875  qt.  to  pints. 

12.  278  pt.  to  gallons,  etc.  16.  13  gal.  to  quarts. 

13.  675  pt.  to  gallons,  etc.  17.  144  gal.  to  pints. 


268 


FIFTH  YEAR 


Dry  Measures 


Dry  measures  are  used  in  measuring  grain,  fruit,  roots,  and 
other  dry  articles.     Name  five  articles  sold  bv  the  bushel. 


2  pints  (pt.) 

=  1  quart  (qt.) 

8  quarts 

=  1  peck  (pk.) 

4  pecks 

=  1  bushel  (bu.) 

1  bushel 

=  2150.42  cubic  inches 

1  bu.  =  4  pk. 

=  32  qt.  =  64  pt. 

1.  Find,  by  measuring,  how  many  pecks  equal  a  bushel. 

2.  How  many  quarts  will  fill  a  peck  measure  ? 

3.  How  many  quarts  will  fill  a  bushel  measure? 

4.  How  many  bushels  do  16  pecks  equal?  64  quarts? 


Written  Work 
Change : 

1.  3  bu.  2  pk.  6  qt.  to  pints.      4.    ^b  pk.  to  bushels. 

2.  96  pt.  to  bushels.  5.    8  bu.  3  pk.  1  pt.  to  pints. 

3.  1200  qt.  to  bushels.  6.    1500  pt.  to  bushels. 


DENOMINATE  NUMBERS 


269 


Avoirdupois  Weight 

The  teacher  should  secure  a  scale  and  weights,  and  have  pupils  weigh 
articles  of  different  kinds. 

Avoirdupois  weight  is  used  in  weighing  heavy  articles ; 
as,  groceries,  coal,  grain,  and  metals,  except  gold  and  silver. 


16  ounces  (oz.) 

=  1  pound  (lb.) 

100  pounds 

=  1  hundredweight  (cwt.) 

20  hundredweight 
2000  pounds 

=  lton(T.) 

2240  lb. 

=  1  long  ton 

1  T.  =  20  cwt. 

=  2000  lb  =  .32,000  oz. 

The  long  ton  is  used  at  the  United  States  custom  houses,  and  in 
wholesale  transactions  in  coal  and  iron. 

The  avoirdupois  pound  contains  7000  grains,  and  the  avoirdupois 
ounce,  437|  grains. 

The  unit  of  avoirdupois  weight  is  the  pound. 


1.  Name  several  kinds  of  articles  sold  by  the  pound;  by 
the  ton. 

2.  How  many  tons  equal  6000  pounds?    24,000  pounds? 

3.  Find  the  cost  of  2^  tons  of  hay  at  1 14  a  ton. 


270 


FIFTH   YEAR 


Change : 

1.  G  lb.  5  oz.  to  ounces. 

2.  3  T.  8  cwt.  to  pounds. 

3.  4  cwt.  3  lb.  to  ounces. 

4.  5|-  cwt.  to  ounces. 

5.  3600  lb.  to  cwt. 


Written  Work 


6.  2  T.  5  lb.  to  ounces. 

7.  544  oz.  to  pounds. 

8.  6000  lb.  to  tons. 

9.  128  oz.  to  pounds. 
10.  810  oz.  to  lb.  and  oz. 


Time  Measures 


Time  measure  is  used  in  measuring  time.     There ^ are  two 
standard  units  of  time,  the  day  and  the  year. 


60  seconds  (sec.) 

=  1  minute  (min.) 

60  minutes 

=  1  hour  (hr.) 

24  hours 

=  1  day  (da.) 

7  days 

=  1  week  (wk.) 

1  year  =  12  mo. 

=  365  or  366  days  = 

52  wk.  1  da 

L.  or  52  wk.  2  da. 

DENOMINATE  NUMBERS  271 

1.  How  many  hours  is  it  from  midnight  on  Tuesday  to 
midnight  on  Wednesday? 

2.  At  what  time  does  the  new  day  begin? 

3.  How  many  times  in  a  day  does  the  hour  hand  pass 
around  the  face  of  the  clock? 

4.  What  part  of  an  hour  are  10  minutes?  45  min.? 

5.  What  part  of  a  minute  are  15  seconds?  30  sec? 

6.  What  do  you  mean  by  A.M.  ?  by  p.m.  ?  by  M.  ? 

7.  Read  the  time  on  each  of  the  clocks  in  the  picture. 

8.  A  man  leaves  home  at  6:30  A.M.  and  returns  at 
5:45  P.M.     How  long  is  he  away  from  home? 

9.  A  train  leaves  the  station  at  11:10.  It  requires  25 
minutes  to  reach  the  station.  At  what  time  must  one  leave 
home  in  order  to  catch  this  train? 

10.  Harry  leaves  for  school  at  8:30,  and  reaches  school 
at  3  minutes  before  9  o'clock.      How  long  is  he  on  the  way? 

11.  The  morning  session  of  school  begins  at  9  A.M.  and 
closes  at  11:30  a.m.  The  afternoon  session  begins  at  1  P.M. 
and  closes  at  3:45  p.m.     How  long  are  both  sessions? 

12.  How  many  months  have  31  days  each?  30  days  each? 
28  days?     When  has  February  29  days? 


Written  Work 

Change: 

1.  3  hr.  6  min.  to  seconds.  5.  12  wk.  6  da.  to  hours. 

2.  144,000  sec.  to  days.  6.  336  hr.  to  weeks. 

3.  5  da.  3  hr.  to  minutes.  7.  5760  min.  to  days. 

4.  108  mo.  to  days.  8.  30  days  to  seconds. 

9.    If  the  school  is  in  session  5J  hours,  how  many  seconds 
is  it  in  session? 


272 


FIFTH   YEAR 


10.  At  $1J  a  day,  how  much  will  a  boy  earn  in  14  days? 

11.  If  a  motorman  receives  20  ^  an  hour,  what  is  his  pay 
for  6  days  of  9  hours  each? 

12.  A  clerk  pays  f  4.50  a  week  for  board.     How  much  will 
his  board  cost  him  for  September,  October,  and  November  ? 

13.  At  the  rate  of  f  |  a  day,  how  much  can  a  boy  earn 
during  the  month  of  February? 


Distance 


The  teacher  should  bring  into  the  class  a  yard  stick  and  a  50-foot 
measuring  line.  Each  pupil  should  be  provided  with  a  12-inch  ruler, 
with  inches  and  half  inches  clearly  marked. 

Linear  measure  is  used  in  measuring  lines  and  distances. 


12  inches  (in.) 
3  feet 

5|  yards | 
lel  feet  J 
320  rods 


=  1  foot  (ft.) 
=  1  jkrd  (yd.) 

=  1  rod  (rd.) 

=  1  mile  (mi.) 


1  mi.  =  320  rd.  =  1760  yd.  =5280  ft. 


DENOMINATE  NUMBERS 


273 


1.  Measure  the  length  of  a  book ;  of  a  desk  ;  of  a  table. 

2.  Measure  the  yard  stick  with  the  ruler.     How  many- 
feet  equal  a  yard?     A  foot  is  what  part  of  a  yard? 

3.  With  the  measuring  line  mark  off  16|  ft.,  or  1  rod,  on. 
the  blackboard. 

4.  How  many  yards  are  there  in  16J  ft.  ?   in  320  rd.  ? 


Change : 

1.  33  ft.  to  inches. 

2.  12  yd.  to  feet. 

3.  28  rd.  to  yards. 

4.  J  mi.  to  inches. 


Written  Work 


5.  3  yd.  2  ft.  6  in.  to  inches. 

6.  4  rd.  3  yd.  1  ft.  to  fest. 

7.  1728  in.  to  yards. 

8.  198  in.  to  rods. 


Miscellaneous  Measures 


There  are  12  dozen  in  a  gross. 

1.  How  much  will  1  gross  buttons  cost  at  15^  a  dozen? 

2.  A  stationer  bought  12  quires  of  paper  for  f  1.20  and 
sold  it  at  a  cent  a  sheet.     How  much  did  he  gain? 

3.  Find  the  cost  of  40  lemons  at  15  ^  a  dozen. 


274  FIFTH   YEAR 


REVIEW 


1.  A  bicycle  wheel  is  7  feet  4  inches  in  circumference. 
How  many  turns  will  it  make  in  going  6  miles  ? 

2.  How  much  will  3J  bushels  of  plums  cost  at  9  ^  a  quart  ? 

3.  How  much  fence  will  be  needed  to  inclose  a  square 
field,  each  side  of  which  is  22  rods  ? 

4.  If  9  boxes  weigh  27  pounds,  how  mucb  will  36  boxes 
weisfh  ?     How  mucli  will  3  boxes  weis'h? 

5.  George  has  a  can  of  milk  containing  10  gallons.  If  he 
sells  10  quarts  to  his  first  customer,  4  quarts  to  the  second 
customer,  3  gallons  to  the  third  customer,  and  2  gallons 
1  pint  to  the  fourth,  how  much  has  he  left  in  the  can  ? 

6.  How  much  are  5 J  miles  of  telegraph  wire  worth  at 
to. 005  afoot? 

7.  Our  grocer  found  that  9  hams  weighed  82|  pounds. 
What  was  the  average  weight  ? 

8.  How  much  must  be  paid  for  15  gross  of  lead  pencils 
at  35  ^  a  dozen  ? 

9.  Walter  picked  4|  bushels  of  blackberries  and  sold 
them  to  a  grocer  for  6  ^  a  quart.  He  took  in  exchange  eggs 
at  24  ^  a  dozen.     How  many  dozen  did  he  receive  ? 

10.  A  butcher  sold  30^  pounds  of  lard  at  »! 0.12  a  pound, 
and  purchased  with  the  money  flour  at  $0.03  per  pound. 
How  much  flour  did  he  buy  ? 

11.  500  bushels  of  peaches  were  packed  in  baskets,  each 
holding  2  pecks.     How  many  baskets  were  needed  ? 

12.  20  hundredweight  of  starch  was  packed  into  boxes, 
each  containing  5  pounds.  How  much  was  received,  if  each 
box  was  sold  for  6^  ^  ? 


DENOMINATE   NUMBERS  275 

13.  Count  the  change  from  a  five-dollar  bill  for  8  pounds 
of  steak  at  18^  a  pound,  3  cans  of  tomatoes  at  9B^  a  dozen, 
and  2  gallons  of  gasoline  at  15^  a  gallon. 

14.  What  is  my  January  milk  bill,  if  I  use  5  pints  every 
day,  at  8  ^  a  quart  ? 

15.  If  f  of  a  ton  of  coal  costs  13.75,  how  much  will  3 J 
tons  cost  ? 

16.  How  many  pint  cans  can  be  filled  from  26  gallons  of 
tomato  soup  ? 

17.  The  Bell  Telephone  Co.  charges  me  $40  a  year  for 
600  calls.  How  much  is  that  per  month  ?  how  much  for 
each  of  the  calls  ? 

18.  Find  the  amount  of  the  following  sales: 
1  dozen  boxes  of  cocoa  at  15  ^  a  box, 

8  cans  of  tomatoes  at  $  1  a  dozen, 

3  boxes  of  figs  at  8  3  a  dozen, 

11 J  pounds  turkey  at  22  ^  a  pound. 

19.  Five  girls  weigh  75  pounds,  86  pounds,  93  pounds, 
69'  pounds,  and  72  pounds  respectively.  What  is  their 
average  weight  ? 

20.  There  are  20  quires  in  a  ream.  At  $1.20  a  ream,  find 
the  cost  of  3  reams,  3  quires  of  paper. 

21.  How  old  is  a  man  who  is  threescore  years  and  ten  ? 

22.  The  Adams  Coal  Company  sold  8  loads  of  coal  as  fol- 
lows :  2470  lb.,  3680  lb.,  1974  lb.,  2985  lb.,  1741  lb.,  3161  lb., 
3749  lb.,  and  4278  lb.  Find  the  number  of  tons,  hundred 
weight,  and  pounds  sold. 


PRACTICAL   MEASUREMENTS 

LENGTHS  AND  SURFACES 

Lines  that  meet,  making  a  square  corner,  form  a  right 
angle. 

A  figure  that  has  four  straight  sides  and  four  right  angles 
is  called  a  rectangle. 

A  rectangle  having  its  four  sides  equal  is  called  a  square. 

Rectangles  that  are  not  squares  are  sometimes  called  oblongs. 


144 

sq. 

in. 

=  1 

sq. 

ft. 

9 

sq. 

ft. 

=  1 

sq. 

yd. 

4  in. 


The  perimeter  is  the  distance  around  a  surface. 

What  is  meant  by  drawing  a  surface  on  a  scale  ot 
1  inch  to  2  feet  ?     On  what  scale  is  this   surface   drawn  ? 

What  is  the  unit  -of 
measure  ?  How  many 
units   are  there   in    the 

C  WM^I^  ^^^^  ^^^  ^^  squares  ?  in 

cvj  the  second?  How  many 

square  inches  are  there 
in  the  rectangle,  or  what 
is  its  area  ? 


H 

2x4x1 


8  sq.  in.,  area. 


The  area  of  a  rectangle  is  a  number  of  square  units  equal  to 
the  product  of  its  two  dimensions  when  expressed  in  like  units. 

Thus,  if  the  dimensions  of  a  rectangle  are  2  inches  and  4  inches,  the 
area  is  8  square  inches;  if  the  dimensions  are  2  feet  and  4  feet, the  area 
is  8  square  feet. 

276 


PKACTICAL  MEASUREMENTS  277 

Written  Work 

1.  If  a  pane  of  glass  is  10  inches  by  12  inches,  how  many- 
square  inches  does  it  contain  ? 

2.  How  many  square  feet  of  glass  equal  32  such  panes  ? 

3.  A  garden  is  73  feet  by  50  feet.  How  many  square 
feet  does  it  contain  ? 

4.  The  page  of  a  book  is  1\  inches  by  5  inches.  How 
many  square  inches  are  there  on  the  page  ? 

5.  How  many  square  inches  are  there  in  a  page  of  your 
book? 

6.  Measure  the  blackboard  in  your  schoolroom  and  find 
how  many  square  feet  it  contains. 

Note. —  Reduce   inches  to  the  fraction  of  a  foot;    as,  8  ft.  6  in. 

=  8^  ft. 

7.  How  many  square  inches  are  there  in  the  surface  of 
your  schoolroom  door  ? 

8.  At  i  1^  per  square  yard,  how  much  will  it  cost  to 
cover  a  floor  12  feet  by  15  feet  with  linoleum  ? 

9.  A  plate  glass  window  is  9  feet  8  inches  wide  and  12 
feet  3  inches  long.  How  much  will  such  a  window  cost  at 
f  0.36  per  square  foot? 

10.  Brussels  carpet  is  2i  feet  wide.  How  many  square  feet 
are  there  in  a  yard  of  it  ? 

11.  A  room  is  16  feet  long  and  14  feet  wide.  How  much 
will  it  cost  to  paint  the  ceiling  of  this  room  at  12  ^  per  square 
yard? 

12.  Which  is  the  larger,  a  surface  26  in.  long  and  5  in. 
wide  or  a  surface  20  in.  long  and  12  in.  wide  ? 

13.  At  15^  per  square  foot,  how  much  does  a  sidewalk 
50  feet  long  and  5  feet  wide  cost  ? 


278  FIFTH  YEAR 

14.  At  12  ^  per  square  foot,  how  mucli  will  it  cost  to 
cement  the  floor  of  a  cellar  28  ft.  4  in.  by  22  ft.  6  in.  ? 

15.  At  81.05  per  square  yard,  how  much  will  it  cost  to 
pave  the  street  in  front  of  a  50-foot  lot,  the  street  being  33 
feet  wide  between  the  curbs  ? 

16.  Compare  a  square  1  inch  on  a  side  with  a  square  2 
inches  on  a  side.  Prove  your  work  by  drawing  the  required 
squares  and  dividing  tliem  into  square  inches. 

17.  Compare  a  rectangle  2  inches  by  8  inches  with  a  rec- 
tangle 4  inches  by  16  inches. 

18.  Show  that  a  square  4  inches  on  a  side  is  16  times  as 
large  as  a  square  1  inch  on  a  side. 

19.  Name  and  draw  the  figures  you  have  learned  in  which 
all  the  angles  are  right  angles. 

20.  What  other  name  is  sometimes  given  to  a  rectangle  ? 
Is  a  square  a  rectangle  ?  When  is  a  rectangle  not  a  square  ? 
Draw  figure  to  illustrate. 

21.  Name  the  different  measures  of  length. 

22.  Lines  have  what  dimensions  ?  Surfaces  have  what 
dimensions  ?     Illustrate  each. 


VOLUME 

1.  What  is  the  length  of  the 
figure?  the  width?  the  height? 

2.  How    many    dimensions 
has  it  ? 

3.  How  many  sides  or  faces 
has  it  ? 

4.  Show  that  each  side  is  a 
square. 


PRACTICAL   MEASUREMENTS 


279 


5.  How  many  square  surfaces  has  it  ? 

A  solid  with  six  equal  squal-e  surfaces  is  a  cube. 

6.  Look  at  the  figure  and  tell  how  many  edges  it  has. 
What  is  the  length  of  each  edge  ? 

A  cube  whose  edge  is  1  inch  is  called  a  cubic  inch. 

7.  Draw  on  paper  or  on  the  blackboard  a  square  foot. 

8.  Divide  each  side  into  12  equal  parts  and  connect  them 
by  straight  lines. 

9.  How  many  square  inches  equal  a  square  foot  ? 

10.  The  base  of  a  1-inch  cube  has  how  many  square  inches  ? 

11.  144  cubes  1  inch  on  an  edge  can  be  placed  on  a  sur- 
face of  1  square  foot  thus  : 

ift. 


((((((((\(c 


12.  What  is  the  height  of  12  such  layers  of  cubes  ?    How 
many  cubic  inches  are  there  in  the  first  layer  ?  in  12  layers  ? 

13.  How  many  cubic  inches  can  be  placed  in  the  cube  ? 


1728  cubic  inches  (cu.  in.)=  1  cubic  foot  (cu.  ft.) 


280 


FIFTH  YEAR 


SURFACES  AND  VOLUMES 


3  ft. 


1.  How  many  feet  on  an  edge  is  the  cube  in  the  figure 
above  ? 

2.  How  many  cubes  1  foot  on  an  edge  are  there  in  the 
first  layer  ? 

3.  How  many  cubes  1  foot  on  an  edge  are  there  in  the 
3  layers? 


27  cu.  ft.  =  1  cubic  yard  (cu.  yd.) 
A  cart  load  of  earth  =  1  cu.  yd. 


The  contents,  or  volume,  of  any  body  that  has  six  rectangular 
surfaces  is  a  number  of  cubic  units  equal  to  the  product  of  its 
three  dimensions  when  expressed  in  like  units. 

4.  A  schoolroom  is  30  ft.  wide,  40  ft.  long,  and  16  ft. 
high.     Find  the  number  of  cubic  feet  of  air  in  it. 

5.  Find  the  number  of  cubic  yards  of  air  in  the  room. 

6.  A  piece  of  timber  is  1  ft.  square  at  the  end  and  12  ft. 
long.     How  many  cubic  feet  are  there  in  it  ? 


PRACTICAL  MEASUREMENTS 


281 


7.  How  many  l-in.  cubes  are  necessary  to  make  a  rec- 
tangular solid  12  in.  long,  8  in.  wide,  and  4  in.  high  ? 

8.  A  box  is  4  ft.  long,  2  ft.  wide,  and  2  ft.  high.     Find 
the  number  of  square  feet  in  its  six  surfaces. 

9.  Find  the  number  of  cubic  inches  in  the  box. 

10.  A  bin  for  grain  is  12  ft.  long,  8  ft.  wide,  and  5  ft.  deep. 
Find  the  number  of  cubic  feet  in  it. 

11.  If  there  are  2150.42  cu.  in.  in  a  bushel  of  wheat,  find 
the  number  of  bushels  of  wheat  the  bin  will  hold. 

12.  A  water  tank  is  8  ft.  long,  4  ft.  wide,  and  3  ft.  deep. 
If  a  cubic  foot  of  water  weighs  62|  lb.,  find  the  weight  of  the 
water  when  the  tank  is  full. 

13.  A  stone  wall  is  4ft  ft.  long,  4  ft.  high,  and  2  ft.  thick. 
Find  the  number  of  cubic  feet  of  stone  in  it. 

14.  Measure  the  dimensions 
of  your  schoolroom  and  find  the 
number  of  cubic  feet  of  air  in  it. 

15.  A  rectangular  solid  is 
1  ft.  square  and  4  ft.  long.  Find 
the  surface  of  its  six  faces. 

16.  Cut  from  cardboard  a 
surface  as  shown  in  the  draw- 
ing. Fold  along  the  dotted 
lines  into  a  box;  find  the  sur- 
face of  the  six  faces  and  the 
contents  of  the  box  in  cubic 
inches. 

17.  Measure  the  walls  and  ceiling  of  your  schoolroom  and 
find  the  cost  of  plastering  them  at  27  cents  per  square  yard. 

18.  Cut  from  cardboard  a  diagram  to  show  a  rectangular 
box  18  in.  long,  12  in.  wide,  and  8  in.  deep. 


lin. 

• 

282 


FIFTH   YEAR 


How  many  cubic 
How  many  cubic 
How  many  cubic 


19.  Find  the  number  of  cubic  inches  in  the  box/ 

20.  Measure  the  surface  of  your  schoolroom  floor,  and 
find  the  cost  of  oiling  it  at  12  cents  per  square  yard. 

21.  What  is  the  difference  in  cubic  feet  between  9  cubic 
feet  and  a  cube  3  feet  on  an  edge  ? 

To  THE  Teacher.  —  Get,  if  possible,  141  cubical  blocks  1  inch  on  an 
3dge. 

22.  Build  a  cube  3  blocks  on  an  edge. 
Inches  are  there  in  the  cube  ? 

23.  Build  a  cube  4  blocks  on  an  edge, 
inches  are  there  in  the  cube  ? 

24.  Build  a  cube  2  blocks  on  an  edge, 
inches  are  there  in  the  cube  ? 

25.  The  cube  4  blocks  on  an  edge  is  how  many  times  the 
cube  2  blocks  on  an  edge  ? 

26.  Build  a  rectangular  solid  as 
shown  in  the  figure.  How  many 
cubic  inches  are  there  in  the  solid  ? 

27.  Show  that  the  solid  in  problem 
24  has  6  rectangular  surfaces.  Find 
the  surface  of  each  rectangle. 

28.  Build  a  cube  5  inches  on  an  edge.  How  many  more 
than  100  cubes  are  needed  ? 

29.  Find  the  cost,  at  30  cents  a  cart  load  (1  cubic  yard), 
for  excavating  the  ground  for  a  cellar  30  ft.  in  length,  20  ft. 
in  width,  and  4  ft.  in  depth. 

30.  A  laborer  digs  a  ditch  100  ft.  long,  18  in.  wide, 
and  2J  ft.  deep  in  1  day.  Find  the  number  of  cart  loads  of 
3arth  removed,  and  the  cost  at  30  cents  a  load. 


3  in. 


GENERAL  REVIEW 

1.  A  clerk  bought  a  gross  of  penholders  for  80  cents  and 
sold  them  at  2  cents  each.     How  much  did  he  gam  ? 

2.  I  paid  $3.65  for  groceries,  $1.75  for  dry  goods,  and 
87  cents  for  sundries.     What  was  the  cost  of  all  ? 

3.  Write  one  hundred  two  thousand,  seven  hundred. 

4.  Find  the  cost  of  30  gross  of  writing  tablets  at  37J  cents 
a  dozen. 

5.  If  11|  is  subtracted  from  a  certain  number  1^  will 
remain.     What  is  the  number  ? 

6.  A  merchant  pays  6|^  a  yard  for  muslin  and  sells  it 
for  7^^  a  yard.     What  is  his  gain  on  24  yards  ? 

7.  I  can  make  3  aprons  in  6  hours.     How  many  aprons 
can  I  make  in  12  hours  ? 

8.  Write  in  words  4006.015. 

9.  A  man  bought  J  of  a  farm  containing  800  acres  and 
sold  .25  of  his  share.     How  many  acres  had  he  left  ? 

10.  If  8  loads  of  hay  cost  $80,  what  is  the  cost  of  24  loads  ? 

11.  Change  12  gallons,  2  quarts,  1  pint,  to  pints. 

12.  Robert  rides  14.75  miles  north  on  his  pony,  and  his 
brother  James  rides  20.25  miles  south.  How  far  apart  are 
they  at  the  end  of  the  ride  ? 

13.  At  Home's  sale  a  customer  bought  three  remnants  of 
silk,  containing  respectively  16 J  yd.,  12  yd.,  and  9^  yd. 
How  many  yards  of  silk  did  the  customer  buy  ? 

283 


284  FIFTH  YEAR 

14.  There  are  5280  feet  in  a  mile.  How  many  feet  is  it 
from  Albany  to  New  York,  a  distance  of  143  miles  ? 

15.  6  is  y^2  of  what  number  ? 

16.  At  150  a  month  rent,  what  is  the  income  to  the  owner 
on  24  houses  for  12  months  ? 

17.  At  95  cents  per  square  yard,  how  much  will  it  cost  to 
cement  the  floor  of  a  cellar  10  yards  long  and  6  j^ards  wide  ? 

18.  Find  the  cost  of  144  lb.  of  raisins  at  8|^  a  pouncj^. 

19.  Add  8  bu.  1  pk.  3  qt. 

4  bu.  3  pk.  2  qt. 
2  bu.  1  pk.  5  qt. 

20.  Find  the  interest  on  a  loan  of  $  250  made  for  2  years 
and  9  months  at  6  % . 

21.  Explain  why  it  is  wrong  to  say  12  times  325  yards. 

22.  How  many  feet  of  picture  molding  will  be  required 
for  a  room  18  ft.  long  and  12  ft.  wide?  At  6^/  a  foot,  how 
much  will  it  cost  ? 

23.  Change  |,  |,  and  -j^  to  24ths. 

24.  Add  |,  |,  J,  and  ^^, 

25.  Add  by  3's  to  64. 

26.  32  x9|  yards  =  ? 

27.  Change  8  square  rods  to  a  fraction  of  an  acre ;  to  a 

decimal  of  an  acre. 

28.  Each  of  8  boxes  holds  5  pounds, 4  ounces  of  meal. 
How  much  do  all  the  boxes  hold  ? 

29.  What  is  the  cost  of  8  barrels  of  vinegar,  averaging  41 
gallons  3  quarts  per  barrel,  at  18^  a  gallon? 

30.  In  a  warehouse  there  are  15  pillars  2  ft.  by  18  in.,  and 
20  ft.  high.     How  many  cubic  feet  are  there  in  the  pillars  ? 


GENERAL  REVIEW  285 

31.  How  much  will  it  cost,  at  27^  a  square  yard,  to  paint 
a  floor  that  is  18  ft.  long  and  16  ft.  wide  ? 

32.  In  the  first  column  find  the  number  of  yards ;  in  the 
second,  the  number  of  gallons ;  and  in  the  third,  the  number 
of  bushels. 


Cost 

Price 

Cost 

Price 

Cost 

Price 

per  yd. 

per  gal. 

per  bu. 

$3.20 

6i^ 

$45.00 

62-J^ 

$9.00 

75^ 

$6.72 

12J^ 

$36.60 

16f/ 

$15.00 

m^ 

$8.40 

20^ 

$40.50 

m 

$21.75 

37  J/ 

33.  Charles  spent  at  a  sale  5  half  dollars,  6  quarters,  3 
dimes,  4  nickels,  and  3  pennies.  How  much  did  he  spend  in 
all? 

34.  A  motorman  worked  8 J  hours  one  day,  and  10|-  hours 
another  day.  At  24^  an  hour,  how  much  did  he  receive  for 
the  two  days'  work  ? 

35.  If  12  T.  of  hay  cost  $144,  how  much  will  24  T.  cost  ? 

36.  How  many  pounds  of  sugar,  at  $0.06  a  pound,  can  be 
exchanged  for  9  pounds  of  butter  at  $0.32  a  pound,  and  12 
dozen  eggs  at  $0.18  a  dozen  ? 

37.  William  works  6|  hours  on  each  of  36  Saturdays. 
Find  the  amount  earned  at  12  ^  per  hour. 

38.  John  earned  $350  and  loaned  it  for  1  yr.  and  8  mo.  at 
5  %  interest.     What  was  the  amount  when  due  ? 

39.  If  it  takes  16 J  yards  to  make  a  dress,  how  many  yards 
will  it  take  to  make  12  dresses? 

40.  How  much  will  128  clocks  cost  if  8  clocks  cost  $104? 

41.  A  lady  sold  some  butter  at  $0.32  a  pound  and  with 
the  sum  received  bought  16  yards  of  cloth  at  90^  a  yard,  4 
hats  at  $3  each,  4  ties  at  24^  each,  and  4  pairs  of  gloves 
at  55^  each.     How  many  pounds  of  butter  did  she  sell? 


^86  ■  FIFIH    YEAR 

42.  A  father  having  8105.06  gave  197.08  to  his  son.  If 
he  divided  the  remaining  amount  equally  between  his  two 
daughters,  how  much  did  each  receive  ? 

43.  Find  the  cost  of  81.25  acres  of  land  at  $46.75  an  acre. 

44.  At  $0,525  per  bushel,  how  much  corn  can  be  bought 
for  152.50? 

45.  A  dressmaker  had  40  yd.  of  cloth.  She  used  12^ 
yd.  for  a  dress,  3|  yd.  for  a  coat,  and  S^  yd.  for  a  waist. 
How  many  yards  had  she  left  ? 

46.  Mr.  White  owned  |  of  a  farm.  He  sold  J  of  his  share 
at  160  an  acre.  If  the  entire  farm  contained  80  acres,  how 
much  money  did  he  receive  ? 

47.  At  121  cents  a  dozen,  how  much  will  |  of  16  dozen 
buttons  cost? 

48.  If  I  of  a  dozen  oranges  cost  20  cents,  how  much  will 
5J  dozen  cost  ? 

49.  A  company  of  four  men  leased  a  tract  of  West  Vir- 
ginia land  and  drilled  an  oil  well.  It  flowed  for  a  time 
at  the  rate  of  100  barrels  a  day.  If  oil  was  selling  at  $1.68 
a  barrel,  how  much  did  each  realize  per  day  ? 

50.  I  paid  $6.30  for  ribbon.  If  I  paid  60^  for  f  of  a  yard, 
how  many  yards  did  I  buy  ? 

51.  A  farmer  lent  his  nephew  $450  for  2  years  and  6 
months  at  6%.     Find  the  interest. 

52.  A  bought  a  horse  for  $100,  a  cow  for  $45-|-,  and  a 
wagon  for  $78|.     What  was  the  cost  of  all  ? 

53.  $65  is  the  value  of  |-  of  an  acre  of  land.  At  this  rate 
how  many  acres  of  land  can  be  bought  for  $  6396  ? 

54.  Change  27000  pounds  to  tons. 

55.  One  side  of  a  square  is  18  ft.  8  in.  What  is  the  dis- 
tance around  it  ? 


GENERAL  REVIEW  287 

56.  If  I  spend  $  I  for  an  inkstand,  $|  for  a  book,  and  $^ 
for  paper,  how  much  do  I  spend  in  all  ? 

57.  Lucy  has  1^,  and  Mary  $|.  Which  has  the  larger 
sum,  and  how  much  larger  is  it  ? 

58.  Charles  earned  il7J,  John  120},  and  William  i25J. 
How  much  more  must  they  earn  to  have  $  75  in  all? 

5x3  75 

59.  Perform  the  operations  indicated  :    — - — '-^—^. 

60.  On  Jan.  1,  1906,  Mr.  Blethrow  bought  of  T.  C.  Jen- 
kins &  Co.,  the  following: 

25  bbl.  of  flour,  @  $   5.25 

20  bbl.  of  sugar,  @  14.50 

29  hams,  @  1.85 

112  lb.  of  bacon,  @  0.10 

Find  total,  and  receipt  the  bill,  acting  as  clerk  for  T.  C. 
Jenkins  &  Co.  yourself. 

61.  How  many  pecks  are  there  in  17J  bushels  ? 

62.  (.5  +  .75)-i-.00125=? 

63.  In  an  orchard  there  are  144  trees ;  18  are  cherry,  36 
are  apple,  and  ^  of  the  remainder  are  peach  trees.  How 
many  are  peach  trees? 

64.  How  many  pecks  are  there  in  25  bu.  3  pk.  ? 

65.  Find  the  cost  of  21 1  bushels  wheat  at  80  ^  a  bushel. 

66.  1  ton  of  coal  will  cost  how  many  times  as  much  as  5 
hundredweight?  as  600  pounds?  as  60  pounds? 

67.  A  haystack  contains  9000  pounds  of  hay.  How  much 
is  it  worth  at  $  15  a  ton? 

68.  A  grocer  bought  5  barrels  of  cider  at  $6.50  a  barrel, 
and  sold  it  at  $  0.10  a  quart.     How  much  did  he  gain  ? 


288  FIFTH   YEAR 

69.  A  farmer  exchanged  45  pounds  of  butter,  at  30  cents  a 
pound,  for  sugar,  at  5  cents  a  pound.  How  many  pounds 
of  sugar  did  he  receive  ? 

70.  How  many  cubic  feet  of  air  are  there  in  a  room  12  ft. 
long,  10 J  ft.  wide,  and  9  ft.  high? 

71.  What  is  the  cost  of  48  gal.  oil  at  5  cents  a  quart  ? 

72.  For  i  20^,  how  many  barrels,  at  $  2^  a  barrel,  can  be 
bought  ? 

73.  A  boy  lost  J  of  his  marbles  one  day,  ^  of  them  the  next 
day,  and  had  44  marbles  left.     How  many  had  he  at  first  ? 

74.  John  had  120  marbles.  He  gave  Louis  |  of  them,  and 
Henry  J  of  the  remainder.     How  many  had  he  remaining  ? 

75.  If  a  boy  pays  $2.50  a  hundred  for  papers,  and  sells 
them  for  5  cents  apiece,  how  much  does  he  gain  on  300 
papers  ? 

76.  A  field  contains  25  rows  of  corn.  If  each  row  yields 
6  bu.  3  pk.,  how  much  corn  will  the  field  yield? 

77.  What  will  be  the  cost  of  painting  the  ceiling  and  the 
floor  of  a  kitchen  14  ft.  long  and  12  ft.  wide,  at  iO.lO  per 
square  yard  ? 

78.  Mary  has  §175.  How  mtich  will  it  amount  to  in  3 
years  and  10  months  at  6  %  ? 

79.  How  many  loads  of  earth  will  be  removed  in  excavating 
a  cellar  24  ft.  long,  18  ft.  wide,  and  6  ft.  deep? 

80.  Add  one  and  one  tenth,  one  and  one  thousandth,  one 
hundred  and  one  thousandth,  ten  and  five  hundredths,  and 
six  tenths. 

81.  Frank  worked  2J  hours  for  five  days  each  week  and 
12  hours  each  Saturday.  Find  his  earnings  for  10  weeks 
at  12^  an  hour. 


ANSWEKS 

THIRD   YEAR 

Page  32.  — 2.  a.  994  ;  &.  820  ;  c.  781 ;  <?.  1204  ;  e.  831  ;  /.  755. 
3.  a.   1005;  b.   853;  c.  1733;  d.   1442;  e.   1490;  /.  1932.   4.  a.   908; 

b.  962;   c.  954;  d.   1334;   e.  189;   f.   757.   6.  a.  1397;  b.   1©06 ; 

c.  1338;  d  1292;  e.   1414;  /.  1757. 

Page  33.  — 1.  a.   38;  &.  44;  c.  34;  d.  32;  e.   30;  /.  38;  ^.  41; 

h.   41  ;  I.  42  ;  j.   32 ;  k.   45  ;  Z.  46  ;  m.  34 ;  n    32.  2.  a.   784  ;  6.  1118 ; 

c.  2040;  d.  1196;  e.  553;  /.  1235;  ^.  561.  3.  a.    2050;  &.  1397;. 

c.  1433;  d  1609;  e.  1509;  /.  1695;  gr.  994.  4.  a.  1411;  6.  2020; 
c.  1325;  (Z.  838;  e.   1654;  /.  706;  ^.  1037. 

Page  34.  — 2.  a.   3095;   ft.  3494;  c.   7421;  d  1763;  e.    10,388. 

3.  a.  7783;  b.   5778;  c.  10,805;  d.  14.553;  e.  11,997.   4.  a.  12,640; 

b.  13,239;     c.  9715;     d.  5610;     e.  12,803.     6.    27.     6.  26.     7.    33.     8.  35. 
Page  35.  — 1.    600.     2.    1044.     3.    4631.     4.    3004.      5.    1305.      6.    800. 

7.   834.       8.    1175^.       9.    8654.      10.    187  pt.       11.    1159  qt.      12.    1109  pk. 
13.    1330  in.     14.    4364  dimes.     15.    5627  hr.     16.    2239  min.     17.    3153  gal. 
18.    3882  da. 
Page  36.  — 1.    22,595.     2.    19,999.      3.    14,177.     4.    19.265.     5.    15,189. 

6.  24,973.  7.  22,;-).:7.  8.  23,289.  9.  23,320.  10.  15.873.  11.  36  men. 
12.    $676.     13.    774  mi.     14.    787  bii.     15.    $678. 

Page  41.-5.   87  boys.    6.   27  chickens.    7.  209  mi.    8.   7  ft.     9.   167  mi. 

Page  42.  — 1.    3749  pupils.        2.    8625.        3.    3712  ft.        4.    4385  people. 

5.  1511  boys.     6.    5437  flags.     7.    430  steps.     8.    390  fares. 

Page  54.  — 2.    86.06;     85  60;     84.49;     86.07;     85.68.  3.    $22.35. 

4.  $23.54.  6.  $24.73.  1st  col. :  $9.62  ;  2d  col.  :  $10.92  ;  3d  col. :  $11.87  ; 
4th  col.:  $13.93;  5th  col.  :  $8.24;  6th  col.:  $16.04.     6.    a.  $2.21;   b.  $.51; 

c.  $.85;  (Z.  $3.46;  c.  $2.48.  7.  a.  $.96;  &.  $1.79;  c.  $1.25;  d.  $.85; 
e.  $2.57.     8.   $6.89.    9.    $5.78.     10.   $3.90.     11.    $4.82. 

Page  55.  — 1.  a.  $913.87;  &.  $2489.87  ;  c.  $2269.27;  f7.  $2624.92. 
2.  a.  $1444.03;  6.  $1521.75;  c.  $1347.07;  <?.  $902.09.  3.  $1671.24. 
4.  $873.44.  5.  $1292.77.  6.  $835.82.  1st  col. :  $1412.07;  2d  col. : 
$172.80;      3d  col. :      $1244.99;     4th  col.:  $  1843.41.  Total,  $4673.27. 

7.  a.  $279.08;  b.  8256.29;  c.  8242.91;  d.  $626.04.    8.  a.  $97.77;  b.  $28.39; 

c.  $167.51;  d.  $138.60.     9.    $71.62.     10.   $65.82. 

Page  63.  — 1.  a.  16,910;  b.  20.524;  c.  19,634;  d.  18,184;  e.  13,022. 
2.  a.  18,330;  b.  15,900;  c.  16,996';  d.  22,750;  e.  21,607.  3.  a.  21,010; 
b.  24,150;   c.  24,153;   d.  26,261;   e.  26,350. 

Page  64.-2.  a.   3136;  b.   5591;  c.  3239  ;  d.  1812;  e.  2541.  3.  a.   1084; 

6.  22i>3;  c.  4986;  d.   1766;  e.   3844.    4.  a.   3939;  b.   2814;  c.  1285; 

d.  1832  ;  e.   4809.     5.  a.   3226  ;  6.  1778  ;  c.   1343  ;  d.   2244  ;  e.  950. 

e.  a.   3058  ;  b.   206  ;  c.  2429  ;  d.   2291  ;  e.   2215.   7.  6908 ;  6921. 


290  ANSWERS 

Page  65.  — 1.  a.   1869;  b.   819;  c.  2(589;  d.   3479;  e.  659.   2.  n.   1706 

6.  1599;  c.  1888;  d.   494;  e.  408.    3.  a.    2059;  Z>.  1505;  c.   8699 
d  948  ;  e.  955.  4.  a.  3579 ;  b.   4065 ;  c.  489 ;  d.   995 ;  e.   2764.  5.  a.  749 
b.   947;  c.  2105;  (Z.  3805;  e.  3736.     6.  a.  3676;  b.   487;  c.  4405 
d.   4006 ;  e.  4798.     7.  a.  4098 ;  6.  769 ;  c.  526 ;  d.    2069  :  e  1854.' 
8.  a.   3657  ;  6.  999 ;  c.  604 ;  d.   892  ;  e.  3775. 

Page  73.  — 1.  a.  $1447.28;  b.  $984.34;  c.  $1180.93;  d.  $1572.63. 
2v  a.   $154.56;  b.    $97.75;  c.  $76.78;  d.   $140.21.       3.  $9737.98. 

4.  $1098.36.     5.  $982.04.     6.  a.   $57.18;  6.  $145.71;  c.   $174.67; 

d.  $90.51;  e.  $216.72.  7.  a.  $356.59;  6.  $93.58;  c.  $37.98;  d.  $733.47; 

e.  $90.  8.  $190.35.  9.  $250.78.  10.  $272.27.  11.  $261.62. 
12.  $119.37.    13.  $89.91. 

Page  74.-4.  4i  gal.  5.  7  bu.  6.  10  yd.  7.  4  qt.  9.  35i.  10.  55i. 
11.  79^.  12.  133.  13.  6;  8;  1;  4;  9;  9A.  14.  3*  ;  U ;  2 ;  2  ;  7  ;  8. 
1£.  17  ;  8  ;  7  ;  13  ;  25^  ;  23. 

Page  75.-3.  a.  7  ;  6.  8  ;  c.  9i ;  d  13f ;  e.  17.  4.  a.  31 ;  6.  23  ;  c.  23; 

d.   22  ;  c.  30.  5.  3  ;  5i ;  5| ;  3^  ;  3.   6.  4f  ;  3^  ;  5  ;  13  ;  8.   7.  3  inches. 

Page  76.— 2.  $3.   8.  6^.   4.  7  gal.   5.  5f  pk.   6.  9  bu.   7.  9  hr. 

8.  a.  11  ;  b.  23;  c.  36| ;  d.  20f  ;  e.  27;  /.  30.  9.  a.  52i ;  b.  57;  c.  90; 
d.  2;  e.  29;  f.  60.  10.  5^.  11.  2.  12.  5.  13.  4.  ^14.  7.  15.  6i. 
16.  H.  17.  'll^.  18.  16.  19.  H.  20.  9.  21.  1.  22.  12^.  23.  8^. 
24.  7|. 

Page  77. —1.  6  tons.   2.  6^  gallons.   3.  1625|  gallons.   4.  59  bu. 

5.  2ibu.  6.  11  yards.  7.  8  yards.  8.  $288.  9.  92  1b.  10.  U  gal. 
11.  69  ft. 

Page  81. —1.  120  feet.  2.  $20.  3.  $26.  4.  $156.  6.  41.  6.  $36. 

7.  $400.  8.  $22.24. 

Page  84.  — 2.  60.  3.  84.  4.  408.  5.  714.  6.  390.  7.  990.  8.  2464. 

9.  1023.  10.  2576.  11.  2322.  12.  1476.  13.  1728.  14.  2223.  15.  1591. 
16.  6045.  17.  2530.  18.  2009.  19.  3776.  20.  $1.02.  21.  $5.  22.  $9.90. 
23.  $1.20.  24.  $1.50.  25.  $3.51.  26.  $2.03.  27.  $2.70.  28.  $1.68. 
29.  $2.64.  30.  $1.04.  31.  $2.90.  32.  50)^.  33.  $2.55. 

Page  89.  — 1.  28  yd.  2.  $2.24.  3.  19  caps.  4.  30  pupils.  5.  $1.26. 
€.  $5.74.  7.  $4.45. 

Page  91.— 1.    a.  $75.06;   b.  $87.08;   c.  $66.01;  d.   $75.26;    e.    $52.03. 

2.  a.  Mon.  $163.61;  b.  Tues.  $181.53;  c.  Wed.  $156.05;  d.  Thurs. 
$241.92;  e.  Fri.  $255.09.  Total,  $998.20.  Corn:  $323.45;  oats: 
$128.76;    bran:  $35.95;    chop:  $69.89;    meal:    $46.40;    flour:    $393.75. 

3.  $3595.55.    4.  $11.55. 

Page  92.-3.  a.  2987  ;  b.   2695  ;  c.  1197  ;  d.  991 ;  e.  172.    4.  a.  6503  ; 

b.   240;  c.  1791;  d.   5098;  e.  1363.      5.  a.   1100;  b.   3631;  c.   3619; 

d.  1414;  e.  203.  6.  a.  3695;  6.  1070;  c.  1192  ;  d.  2504;  e.  4893. 
7.  a.   2097 ;  5.  2802 ;  c.  295 ;  d.   1308 ;  e.  1503. 


ANSWERS  291 


Page  93.— 28.    a.  18,808;    h.  21,710;   c.  32,740;    d.  27,171;   e.  27,189. 
3.   «.  20,327  ;    b.  26,902  ;   c.  34,134  ;   d.  30,398  ;  e.  24,095. 


Page  94.  — 1.  104  feet.         2.   $38.60.         3.14.05.         4.    320  minutes. 

6.  $5.25.  6.    §32.25. 

Page  95.— 28.  2143.  29.  6639.         30.  3332.  31.  1553.  32.  1002. 

33.  6168.           34.  5770.  35.  2522.         36.  2226.  37.  917.  38.  2042. 

39.  2660.           40.  4791.  41.  4414.         42.  4563.  43.  1494.  44.  3357. 

45.  1963.          46.  4207.  47.   1055.         48.  3042.  49.  3523.  60.  3274. 
61.   741.     58.  4584.     53.  2120.     54.  3809. 

Page  97.— 7.  40^.      8.  824.      9.  $12.       10.  30j^.      12.  $960.      13.  $30. 

14.  $195.     15.  $9.     16.  $255. 

Page  102.  — 1.  $20.  2.  $1.26.  3.  $2.75.  4.  $2.24.  5.  $15.75. 
6.  .S48.60.  7.  $2.  8.  $6.80.  9.  $15.75.  10.  $16.87|.  11.  $1.96. 
12.  $14.25.       13.  $12.       14.  $9.96.       15.  $114.50.       16.  $3.74. 

Page  103.  — 1.  288  pints.  2.  2.34  miles.  3.  $2.64.  4.  3  hours.  5.  55^. 
6.  23  pounds.  7.  21  plants.  8.  34  weeks.  9.  340  sheep.  10.  $2.16. 
11.  99  bushels.      12.  99  gallons.      13.  131  tons.     14.  32  quarts,  or  8  gallons. 

Pagel04.  — 15.  209  boxes.  16.  $125.  17.  41  weeks.  18.  38  days. 
19.    13  cents.         20.    18  yards.  21.   6  cents.         22.    $2.25.         23.   $24. 

24.   $63.     25.    56^.     26.    $16.     27.    $1.     28.    $21.     29.    $31.50.     30.    96/?. 
31.   $27.     32.    60^     33.    $4.     34.    80^     35.    $20.     36.   $1200. 

PagelOS.  — 37.  7  hours.  38.  1152  sq.  in.  39.  $52.50.  40.  99^. 
41.   $38.         42.    $15.75.         43.    $124.         44.    114  palings.         45.    $1.36. 

46.  $9.60.         47.    $2.         48.   $286.         49.    $2700. 

PagelOe.  — 50.  $2.45.  51.  $1275.  52.  1008  pounds.  53.  $38.25. 
54.  $4.25.  55.  288  pupils.  56.  $270.  57.  $4.08.  58.  $17.60. 
59.   32f  ;  48^         60.   $17.76. 

FOURTH   YEAR 

PagelOS.- 1.    42.000.     2.   66,004.     3.  75,050.     4.  39,122.     5.  210,350. 

6.  565,100.     7.    1,125,000.      8.    3,600,035.      9.   26,009,026.      10.   80,026,064. 
11.    900,009.  12.   46,004,016.  13.    110,000,500.  14.    .336,000,104. 

15.  607,005,006.  16.    17,003,075.  17.    1,002,704.  18.    1,104,186. 
19.   21,110,109.         20.   604,622,468.         21.    101,010,010. 

Pagel09.— 4.   $1050.27.       5.   $904.60.       6.   a.  $108.08;      5.  $228.47; 

c.  $121.79;       d.  $46.3.51.  7.    a.  $602.92;       b.  $766.69;       c.   $437.07; 

d.  $622.92. 

Page  110.  — 2.  846  bu.  3.  $103.  4.  184  da.  5.  $16,995.  6.  $6572. 

7.  108  ft.   8.  444  mi.   9.  $66.91. 

Pagelll.  — 2.  56  yr.  in  1907.  3.  $10,906.  4.  8847  votes.  5-  $4234. 
6.   8224  bu.      7.    6199.      8.   $739.      9.    196  1b.      10.   2669  votes. 


292  ANSWERS 

Page  114.  —3.  First  col.  5580;  5115.  6552  ;  6006.  9408  ;  8624. 
9420  ;  8635.  11,736  ;  10,758.  Second  col.  2832  ;  2596.  9396  ;  8613. 
11,244;  10,307.  6168  ;  5654.  8328  ;  7684.  Third  col.  9468  ;  8679. 
11,136  ;  10,208.  8316  ;  7623.  11,256  ;  10,318.  3552  ;  3256. 

2.  408.  3.  672.  4.  990.  5.  1140.  6.  609.  7.  1331.  8.  2800. 

Page  116.— 4.  248,  rem.  10.  5.  754.  6.  185,  rem.  1.  7.  632,  rem.  2. 
8.  362,  rem.  4.  9.  273,  rem.  4.  10.  811,  rem.  2.  11.  196,  rem.  2 
12.  732,  rem.  5.  13.  6341,  rem.  2.  14.  6642,  rem.  3.  15.  8188,  rem.  6. 
19.  306,  rem.  6.     20.  344,  rem.  7.     21.  581,  rem.  1.     22.  594. 

23.  391,  rem.  1.  24.  651,  rem.  5.  25.  244,  rem.  8.  26.  769,  rem.  10. 
27.  391,  rem.  5.  28.  782.  29.  3516.  30.  6781,  rem.  6.  31.  6162,  rem.  1. 
32.  6888,  rem.  3.  33.  3108.  34.  7656,  rem.  3.  35.  2060,  rem.  6. 
36.  5696,  rem.  7.    37.  6813,  rem.  7.    38.  7697. 

Page  117.  — 1.  $27.  2.  $420.  3.  $36.50.  4.  $15.  5.  $255. 
6.  $15.75.   7.  $7.50.   8.  $23.90.   9.  $950.   10.  $24.75.   11.  $52.25. 

12.  $52.50.   13.  $4.50.   14.  $54.   15.  $4.25.   16.  $8.12.   17.  $1.95. 

18.  $4.50.  19.  8  3.25.  20.  $7.20.   21.  $4.85.  22.  $3.  23.  $2.25. 

24.  $.12.  25.  $3.25.  26.  $1.25.  27.  $3.09.  28.  $.25.  29.  $.15. 
30.  $3.55.  31.  $.04.  32.  $.18.  33.  $.12.  34.  $.75.  35.  $.25. 
36.  $3.50.  37.  $.22.  38.  $.20.  39.  $3.75.  40.  $1.75.  41.  $.11. 
42.  $.20.  43.  $3.25.  44.  $.20. 

Page  118.  — 1.    54  mi.     2.    $33.25.     3.   96  times.      4.  $482.      5.   110  1b. 

6.    $7.20.      7.    $3.70.      8.   $1427.      9.  410  boys. 

Page  119.— 1.   a.  $35,538.46;  h.  $28,736.60;  c.  $30,106.56. 

2.  a.  $21,464.87;     h.  $24,836.37;    c.  $20,168.03.  3.  a.  $20,184.93; 

h.  $21,878.20;    c.  $24,181.02. 

Page  120.— 1.    a.  $681.83;      6.    $748.19;      c.  $614.96;  <?.  $681.68. 

2.    a.  $286.42;     h.   $159.46;     c.  $800.99;     d.  $511.68.         3.  a.  $304.49; 

ft.  $713.35;  c.  $195.01;  cZ.  $366.44.  4.  «.  $784.66;  6.  $812.60; 
c.  $32.45;    cZ.  $233.45.      5.  a.  $412.34  ;    5.  $444.45;    c.  $611.70;   d  $  2.32. 

6.  a.  $611.78;  &.  $256.77  ;  c.  $730.87;  <?.  $663.09.  7.  o.  $642.19; 
7>.  $775.47;  c.  $732.60;  d  $137.96.  8.  a.  $364.93;  6.  $176.05; 
c.  $386.08;     d.  $453.11. 

Pagel23.  — 9.   14,200.        10.    255,000.         11.    980,000.         12.   500,500. 

13.  6940.     14.    12,270.     15.   42,900.     16.   26,320.     17.   42,760.     18.    146,500. 

19.  550,200.  20.  73,600.  21.  477,600.  22.  166.400.  23.  962,000. 
24.   3.576,000.         25.   6,342,000.         26.   6,652,000.         27.  438,000. 

Page  125. -2.  4.  3.  2.  4.  9.  5.  2.  6.  9.  7.  10.  8.  30.  9.  21. 
10.  12.  11.  6.  12.  6.  13.  4.  14.  20  cans.  15.  50  packages. 
16.    5  1b.         17.    120  coats.         18.    35  mo. 

Page  126.  — 6.    a.  1612  ;     &.  20,640  ;     c.  20,712  ;     d  26,775  ;     e.  34,668. 

7.  a.  2254;  h.  18,684;  c.  9136;  d.  39,483;  e.  44,013.  8.  a.  25,972. 
b.  21,bb2  ;     c.  39,015  ;     d.  41,202  ;     e.  31,212. 

Page  127.— 1.  9798.  2.  15,252.  3.  8448.  4.  9824.  5.  11,567. 
6.    8289.       7.    19,368.      8.  46,368.       9.  25,324.      10.  34,790.      11.   23,458. 


13. 
18. 

27. 
34. 


ANSWERS 


28,992.  14.    29,160. 

54,450.  19.   9772. 

23.    304,076.  24 

362,408.         28.   52,780. 
78,792.         35.    66,215. 


15.    77,658. 
20.    10,122. 
287,631. 

29.    73,818. 
36.    85,728. 


293 


16.  54,826. 
21.  432,288. 
25.  355,992. 
30.  133,408. 
37.    828,996. 


441,441.       40.   449,550.        41.   243,404.       42.    361,959. 


346,62.; 


44.   227,864. 


Page  128.  —  5. 
10.    3270  pt.      11. 


8 175.     6. 
10,140  in. 


$957.     7.   $4085.      8.   $17.82. 
12.    656  pk.      13.    6000  oz. 


9.   $27.60. 


Page  129. —1.  $4.20.  2.  $11.16.  3.  $11.76.  4.  $13.05.  5.  $10.32. 
6.  $29.75.  7.  $12.96.  8.  $34.95.  9.  $5.75.  10.  $283.50.  11.  $63.45. 
12.  $229.50.  13.  $83.16.  14.  $37.44.  15.  $41.76.  16.  $609.55. 
17.    $11,440.        18.   $241.92.        19.    226  hr. 


7.  $270. 


8.  $2.80. 


9.  $12 


Page  130.  — 5.  $1.  6.  $.90. 

10.  $.32.         11.  $455.         12.  $324. 

Page  132.  —  6.   21  ;  32  ;  43. 

Page  133.— 1.  12.  2.  25.  3.  41.  4.  34.  5.  31.  6.  17.  7.  24. 
8.  114,  rem  4.  9.  125.  10.  23.  11.  29.  12.  217.  13.  203.  14.  307. 
15.  403.      16.  119,  rem.  30.      17.  32.      18.  207.      19.  62.      20.   71.     21.  33. 


Page  134.— 1.  42.       2. 

43.      3.  24.       4.  S 

8.  21.       9.  37.       10.  29. 

11.  16.       12.  30. 

16.  (5.        17.  25.        18.  24. 

19.  29.        20.  7. 

24.  6.      25.  14.       26.  26. 

27.   17.       28.  19. 

33.  35.      33.  24.      34.  38. 

35.  40.      36.  41. 

40.  32.      41.  33.       42.  44. 

43.  45.      44.  64. 

48.  72.        49.  $36.        50. 

62  da.        51.  16  oz. 

54.  9  hr.       55.  8  words. 

39.       5.  15.       6.  27 
13.  25.        14.  32. 


7.  19. 

15.  42. 

21.  21.       22.  29.       23.  6. 

29.  23.       30.  56.       31.  27. 

37.  31.      38.   160.      39.  220. 

46.  28.      46.  29.       47.  36. 

52.  $1.85.         53.  895  bu. 


Page  135.  — 2.   47.      3.   45,  rem.  18.       4.    62.      5.   77,  rem.  19.      6.    63, 
7.  67,  rem.  18.  8.   83,  rem.  19.  9.   77,  rem.  19.  10.   53,  rem.  61. 

11.  62.  12.  41.  13.  61.  14.  63,  rem.  2.  15.  65,  rem.  44.  16.  77. 
17.  44,  rem.  56.  18.  59,  rem.  60.  19.  47.  20.  76,  rem.  6.  21.  86,  rem.  2. 
22.  83,  rem.  23.  23.  24,  rem.  55.  24.  73,  rem.  76.  25.  183,  rem.  22. 
2G.   310,  rem.  17.        27.    109,  rem.  5.       28.    60,  rem.  32.       29.  52,  rem.  30. 


30.    94,  rem.  84.      31.    106,  rem.  55.       32.   318,  rem.  21.       33. 
'Jl.    92,  rem.  86.       35.   34  suits  ;$ 7  left.       36.    8  bbl. 

123,  rem.  15. 

Page  136.-2.  30  belts.     3.  13  lb.      4.  163  gal.     5.   18  yd. 
-!i|yr.     7.   325  bars.     8.    160  A.     9.    126  trees.     10.   $74.64+. 

6.   35  mo. ; 

Page  137.— 11.    39  bu.         12.    $104.         13.    28  mi. 

Page  138. —1.    $3.37.^       2.    $628.       3.    $64.        4.   $16. 
3.    $36.       7.    $149.64.      8.   $600.      9.   $2080.      10.   $83.25. 
12.    $7.20.          13.    $1024.          14.    $1843.75.         15.    $378. 
17.    $67.86.             18.    $19.             19.    $12.50.           20.    $6.25. 
22.    $6.57.      23.    $12.      24.    $4723.71.      25.    $18,889.06.      26. 
27.   $11,376.97. 

5.  $477. 
11.  $36.40. 
16.    $10.50. 

21.  $30 
$22,479.55 

294  ANSWERS 

Page  139. —  1.  $5.25.  2.  .$4.95.  3.  $3.  4.  $10.  5.  $6.25. 
6.    .$8.         7.   $3.60.         8.   $50.         9.    $145.  10.    $1.90.         11.    $5.25. 

12.   $9.60.     13.    $9.      14.    $18.      15.    $8.     16.   $21.      17.   $32.      18.    $22. 

19.  $  34.     20.    $  16.     21.    $  12.     22.   $  19.     23.    44  mi.     24.    $  .29. 

Page  140.  — 1.  7  cows.  2.  $980.  3.  56  A  ;  $1988.  4.  $2587.20.  6.  $98. 
6.    $242.50.      7.    $540.      8.    $7.      9.   $435.       10.    $532.50.       11.    $22.50. 

Page  141.— 5.   180  sec.    6.   144  hr.     7.   420  min.     8.    78  lir.     9.    76  da. 

10.  91  da. ;  92  da. 

Page  142.  — 4.  6  T.+ 1500  lb.  5.  $.48.  6.  $33.  7.  4000  packages. 
8.    32,000  oz.     9.    l^T. ;  $21. 

Page  144.  — 1.   20  yd.  2.   445Ut.  3.    192  in.  4.    3^  ft. 

6.    5280  ft.       6.   5280  ft.       7.    60  in.     "  8.    10  ft.        9.    24  yd.        10.    35  ft. 

11.  3750  ft.     12.    1980  ft.     13.   228  ft.     14.    5940  rd.      16.   810  yd.  ;  2850  ft. 

Page  146.  —  1.  24  sq.  in.  2.  49  sq.  in.  3.  40  sq.  in.  4.  120  sq.  in. 
5.  64  sq.  in.  6.  144  sq.  in.  7.  81  sq.  in.  8.  100  sq.  in.  9.  15  sq. 
in. ;  16  in.     10.   20  in.  ;  28  in. ;  26  in.  ;  44  in.  ;  32  in.  ;  48  in. ;  36  in. ;  40  in, 

11.  36  sq.  ft.  ;  24  ft.  12.  36  sq.  ft. ;  26  ft.  13.  54  sq.  ft. ;  30  ft.  14.  .30 
sq.  ft.  ;  22  ft.  15.  80  sq.  yd. ;  36  yd.  16.  45  sq.  yd. ;  36  yd.  17.  24  sq. 
yd. ;  28  yd.     18.    20  sq.  yd. ;  18  yd. 

Page  147.— 11.  6606.  12.    2,010,000,004.  13.    75,906. 

14.  1,008,000,075.  15.  84,605,000.  16.  25,038.  17.  900,000,999. 
18.    2,006,030.         19.    1,001,001,000. 

Page  148.— 3.   155.       4.    190.       5.    195.        6.    162.        7.    196;    a.   192; 

b.  384  ;  c.    322.     Total,  898.        8.    121.        9.    217.         10.    152.         11.    189. 

12.  162.     d.    248;  e.    248;  f.   345.     Total,  841.     13.   $186.67.     14.    $60.13. 

15.  $94.87.  16.   $128.80.  17.   $163.36.      a.    $184.08;    1).    $202.51; 

c.  $71.83;  d.   $175.41.      Total,  $633.83.         18.   $480.01.         19.   $520.98. 

20.  $989.32.  21.  $1160.15.  22.  $1036.75.  a.  $342.86;  b.  $319.88; 
c.  $227.50;  d.   $3296.97.        Total,  $4187.21.        23.   54,938. 

Page  149.  — 1.  $29,507.28.    2.  $4644.85.    3.  $3660.64.     4.  $658,373.86. 

5.  $21,684.52. 

Page  150.  — 1.  a.  $3569.11;  6.  $1980.73;  c.  $3351.74  ;  c?.  $1801.11. 
2.    «.  $2578.31;  b.  $4340.01;  c.  $5037.33;  d.  $4154.59.       3.   a.  $3490.40; 

b.  $1.3,565.92;   c.  $3355.63;  d.  $15,631.90. 

Page  151.  — 1.  a.  $211.70;  b.  $128.45;  c.  $3.3,812.37;  d.  $1979.02. 
2.    a.  $310.20;   b.  $227.74;   c.  $15,577.79;   d.   $724.73.       3.    a.  $923.68: 

6.  $596.88;   c.  $17,950.52;   d.   $8694.69.  4.    a.  $387.06;   b.  $218.02. 

c.  $17,619.20;     d.  $2563.59.  5.    a.  $46.06;     b.  $2-3.08;     c.  $148.92; 

d.  $7986.86.  6.   a.    $63;      b.    $51.94;      c.    $129.37;      d.    $5873.8-3. 

7.  a.   $54.85;     b.   $52.05;     c.  $463.54;     d.    $57,529.24.  8.   a.  $8.03; 

b.  $23.52;     c.  $241.08;     d.   $17,879.01.  9.    a.  $52.83;    b.   $72.20; 

c.  $61.44;    d.  $14,140.29. 


ANSWERS 


295 


Page  152.  — 

1.  a.   186,230;   h. 
f.   829,570;    g. 

2.  a.   168,190;   h. 
f.   749,210;    g. 

3.  a.   192,302;   6. 
/.  856,618;    g. 

4.  a.   216,920  ;   h. 
f.   966,280;   g. 

5.  a.   185,350  ;   b. 
f.   825,650;   g. 

6.  a.   212,388  ;   b. 
f.   946,092;   g. 

7.  a.   173,118;   b. 
f.   771,162  ;   g. 

8.  a.   214,830  ;   b. 
f.   956,970;   g. 

9.  a.   107,250  ;   b. 
f.   477,750;   g. 

10.  a.   185,240  ;   b. 
J.   825,160;   g. 

13.  a.    985,  rem.  55  ; 
e.   1177,  rem.  21  ; 

14.  a.    670,  rem.  52  ; 
e.   801  ; 

15.  a.    938.  rem.  52  ; 
e.   1121,  rem.  8; 

16.  a.    589,  rem.  70  ; 
e.    704,  rem.  36  ; 

17.  a.    708,  rem.  37  ; 
e.    846,  rem.  13  ; 

18.  a.  1004,  rem.  68  ; 
e.   1200,  rem.  12  ; 

19.  a.    888,  rem.  44  ; 
e.   1061,  rem.  20  ; 

20  a.    970,  rem.  36  ; 
e.   1159,  rem.  8  ; 


380,925 ; 
474,040  ; 
344,025  ; 
428,120 ; 
393,345 ; 
489,496 ; 
443,700 ; 
552,160; 
379,125; 
471,800 ; 
434,430 ; 
540,624  ; 
354,105  ; 
440,664  ; 
439,425  ; 
546,840  ; 
219,375  ; 
273,000 ; 
378,900  ; 
471,520  ; 
b.  1086, 
/.  1265, 


c.  423,250 
h.  584,085 
c.  382,250 
h.  527,505 
c.  437,050 
A.  603,129 
c.  493,000 
h.  680,340 
c.  421,250 
h.  581,325 
c.  482,700 
h.   666,126 

393,450 

542,961 

488,250 

673,785 

243,750 

336,375 
c.  421,000 
h.   580,980 

c.  931, 


739, 
860, 
1034, 
1204, 
650, 
757, 
781, 
909, 
1107, 
1289, 
979, 
1140, 
b.  1069, 
/.  1245, 


rem.  5/  ; 
rem.  10 ; 
rem.  30 ; 
rem.  52  ; 
rem.  68  ; 
rem.  52  ; 
rem.  24  ; 
rem.  5  ; 
rem.  7  ; 
rem.  22  ; 
rem.  66  ; 
rem.  49  ; 
rem.  50 ; 
rem.  32  ; 
rem.  74  : 


d.  727,990; 

i.  821,105; 

d.  657,470; 

i.  741,565; 

d.  751,726; 

i.  847,877; 

d.  847,960; 

i.  956,420; 

d.  724,550; 

i.  817,225; 

d.  830,244; 

i.  936,438; 

d.  676,734; 

i.  763,293; 

d.  839,790; 

i.  947,205; 

d.  419,250; 

i.  472,875  ; 

d.  724,120; 

i.  816,740; 


1033, 
633, 
703, 
887, 
984, 
557, 
618, 
669, 
742, 
949, 
g.  1053, 
c.  839, 
g.  931, 
c.  917, 


rem.  41  ;  g.  1017, 


rem.  44 
rem.  59 
rem.  69 
rem.  26 
rem.  3 
rem.  32 
rem.  37 
rem.  48 
rem.  46 
rem.  81 
rem.  53 
rem.  66 
rem.  63 
rem.  70 
rem.  9 
rem.  62 


e. 

J- 
e. 

J- 
e. 

J- 
e. 

J- 
e. 

J- 
e. 

J- 

e. 

J- 
e. 

J- 
e. 

J- 

e. 

J- 

1436, 

1304, 

977, 

887, 

1368, 

1241, 

859, 

780, 

1032, 

937, 

1464, 

1329, 

1295, 

1175, 

1414, 

1283, 


643,340 ; 
753,385. 
581,020; 
680,405. 
664,316; 
777,949. 
749,360  ; 
877,540. 
640,300  ; 
749,825. 
733,704  ; 
859,206. 
598,044  ; 
700,341. 
742,140; 
869,085. 
370,500; 
433,875. 
639,920 ; 
749,380. 
rem.  41  ; 
rem.  5. 
rem.  29  ; 
rem.  17. 
rem.  8 ; 
rem.  55. 
rem.  43  ; 
rem.  24. 
rem.  37  ; 
rem.  20. 
rem.  36  ; 
rem.  27. 
rem.  7  ; 
rem.  37. 
rem.  30  ; 
rem.  61. 


Page  153.— 3.  Sum  8| ;  diff.  2^.  4.  Sum  18J  ;  diff.  1|.  5.  Sum  13; 
diff.  6.   6.  Sum  9J  ;  diff.  1^.   7.  Sum  llj;  diff.  6^.   9.  79J.   10.  82J. 

11.  43|.   12.  72. 

Page  154.  — 7.  10|.  8.  25|.  9.  23.  10.  26|.  11.  20|.  13.  Diff.  5^; 
sum  lof.  14.  Diff^Of;  sura  18f.  15.  Diff.  19|;  sum36i.  16.  Diff.  13| ;  sum 
25|.  17.  Diff.  20^  ;  sura  52|.  18.  Diff.  31|;  sum  94.  19.  Diff.  24^;  sura 
103^.    20.  Diff.  2| ;  sum  51|.    21.  Diff.  9| ;  sum  28^.    22.  Diff.  20^  ;  sum  60|. 

Pagel55.  —  3.  Sum  25| ;  diff.  5|.  4.  Sum  42J  ;  diff.  16|.  5.  SumlOlf; 
diff.  61^.  6.  Sura  56| ;  diff.  29f.  7.  Sura  74|  ;^  diff.  50|.  8.  Sum  28^; 
diff.  3^.         9.    Sura  27^  ;  diff.  6f.  10.    Sum  31| ;  diff.  7^.         11.   ^  doz. 

12.  21  hr.      13.   14  ft.      14.  2|  hr. 


296  ANSWEES 

Page  156.  — 2.    178,250.  3.    68,769.  4.   79,232.  5.   143,352. 

6.  .$13,243.75.     7.  $9729.72.     8.  $35,131.86.     9.  $39,363.50.     10.  152,055. 

11.  272,527.  12.  436,792.  13.  925,806.  14.  374,274.  15.  801,975. 
16.   2:>8,717.      17.    791,154.      18.    787,788.      19.    8,166,625.      20.   5,101,995. 

21.  7,349,238.  22.    5,626,836.  23.   5,810,553.  24.    $12,856.25. 

25.  $70,761.42.         26.    $74,017.80.         27.   $34,549.95.         28.    $47,792.88. 

29.  $76,069.08.         30.    $32,388.10. 

Page  157.— 5.    158,632.  6.  84,150.  7.   173,340.  8.    155,342. 

9.  74,844.  10.  357,336.  11.  127,072.  12.  566,820.  13.  $4904.56. 
14.    $24,572.25.     15.    $45,712.80.     16.    $26,742.12. 

Page  158. —  1.    2,179,584.      2.  7,611,881.      3.  4,457,880.     4.  4,086,420. 

5.    2,264,192.       6.    1,248,051.      7.  6,356,256.      8.  2,450,856.      9.  4,569,706. 

10.  6,348,090.  11.  $82,682.10.  12.  $53,352.25.  13.  $  20,693.28. 
14.  $36,042.60.  15.  $39,147.42.  16.  5,751,635.  17.  420,104. 
18.       1,239,150.       19.       2,859,875.           20.      2,209,106.       21.  2,989,472. 

22.  6,167,430.       23.       3,675,846.           24.      4,516,338.       25.  6,308,816. 

26.  6,133,640.       27.      5,381,360.  28.      5,940,102.       29.         6,161,427. 

30.  3,924,462.  81.  6,236,576.  32.  3,490,062.  33.  2,982,640. 
34.  3,183,404.  35.  2,556,048.  36.  1,046,068.  37.  4,606,036. 
38.  3,375,374.  39.  5,407,454.  40.  5,6.32,452.  41.  8,387,215. 
42.  5,286,660.  43.  7,001,232.  44.  4,998,515.  45.  3,901,590. 
46.  433,125  cakes.  47.  907,025 articles.  48.  $430.50.  49.  $105,022.50. 

Page  160.— 2.    630.       3.    1218.        4.    4050.       5.    22,454.       6.    120,428. 

7.  202,460.       8.    182,152|.       9.    386,568.       10.    2,131,272.       11.    3,251,105. 

12.  7,567,812.  13.  2,857,240.  14.  1,690,990.  15.  7,440,372. 
16.    9,414,090.             17.    7,334,634.     .        18.   2,912,529.  19.    8,558,146. 

20.  9,819,096.  21.  6,970,012.  22.  5,229,098.  23.  3,454,723. 
24.  4,793,325.  25.  8,440,432.  26.  5,175,802.  27.  6,452,746. 
28.  4,515,420.  29.  3,410,505.  30.  2,527,020.  31.  1,823,822. 
32.  4,715,126.  33.  6,938,272.  34.  4,816,177.  35.  5,699,174. 

Page  162.  — 9.  a.  504,  rem.  92;  6.  346,  rem.  75;  c.  41.  10.  a.  230, 
rem.  133 ;  h.  322  ;  c.  199,  rem.  90.  11.  a.  339,  rem.  26  ;  6.  256,  rem. 
95 ;  c.  32,  rem.  442.  12.  a.  75,  rem.  236 ;  h.  427,  rem.  m  ;  c.  201,  rem. 
350.  13.    a.   283,  rem.  90;  6.   302,  rem.  247;         c.    215,  rem.  119. 

14.    a.    382,  rem.  103  ;     h.  441,  rem.  136 ;    c.   208,  rem.  220. 

Page  163.  — 2.    446  sheep.       3.    $816.75.      4.   $8615.  p  296 

Page  164.  — 5.  $438.25.  6.  $909.  7.  $27,450.  8.  $  10.91.  9.  $9.04. 
10.    $15.47. 

Page  165.  — 12.   $6020.       13.   8624|  gal.       14.    86.     .15.    602. 

Page  166.  — 17.    $6.16.  18.   525  mi.  19.    36  da.  20.    $984. 

21.  $2.62.       22.    $99.       23.    $348. 

Pagel67.  — 25.  74  A.  26.  50  cows.  27.80  ft.  28.792.  29.  $21. 
30.    40  rings. 

Page  168.  — 32.   $.121.         33.   50  da.  34.   $157.50.         35.  60  da. 

36.   $25.20.      37.    10,976  1b.       38.   $14,700. 


AKSWEKS  297 

Pagel69.  —  39.  26,2081b.  40.  $.25.  41.  2736  bu.  42.  72  books. 
43.  $94.40.  44.  $67.50.  45.  $399.60.  46.  $114.40.  47.  $3.72. 
48.    $813.        49.    $32. 

Page  170.  — 50.  $18.73.  51.   $3.24.  52.  $19.25.  53.  39  da. 

54.   $984.  56.    $26.46.  66.    3280  mi.  57.    $6500.  58.    $726. 

59.    $300. 

Page  171. —1.  377,  rem.  115.  2.  365,  rem.  50.  3.  198,  rem.  24. 
4.  246,  rem.  120.   5.  209,  rem.  279.  6.  232,  rem.  140.  7.  222,  rem.  365. 

8.  194,  rem.  148.  9.  112,  rem.  550.  10.  160,  rem.  424.  11.  100,  rem. 
90.  12.  78,  rem.  635.  13.  141,  rem.  671.  14.  113,  rem.  330.  15.  748, 
rem.  94.  16.  96,  rem.  383.  17.  135,  rem.  36.  18.  122,  rem.  640. 
19.  220,  rem.  8.  20.  130,  rem.  39.  21.  345,  rem.  163.  22.  113, 
rem.  498.  23.  123,  rem.  192.  24.  113,  rem.  183.  25.  336,  rem.  345. 
26.  518,  rem.  272.  27.  1001,  rem.  136.  28.  2107,  rem.  412.  29.  2155, 
rem.  97.  30.  1429,  rem.  516.  31.  1704,  rem.  103.  32.  1390,  rem. 
59.  33.  3551,  rem.  145.  34.  2743,  rem.  302.  35.  1987,  rem.  277. 
36.  3191,  rem.  144.  37.  1005,  rem.  120.  38.  8798,  rem.  56.  39.  7415, 
rem.  12.  40.  1385,  rem.  165.  41.  1242,  rem.  33.  42.  4936,  rem.  60. 
43.  2583,  rem.  15.    44.  2588,  rem.  84. 

Page  172. —  1.  6.  2.  7.  3.  9.  4.  21.  5.  55.  6.  95.  7.  100.  8.  19. 

Page  173.— 2.  96^.  3.81.20.  4.  $3.50.  5.  $45.  6.  42  mi.  8.  20j?. 

9.  $3.  10.  $3.  11.  $41.  12.  4^. 

Page  174. —  1.  6  pencils.  2.  8  yd.  3.  9qt.  5.  $1.36.  6.  $80. 
8.  $1.60.    9.  60^.    10.  $4.80. 

Page  175. —  10.  $60.  11.  $1.50.  12.  $2|.  13.  $.90.  14.  $150. 
15.  $22.80;  15  yd. 

Pagel76.— 16.  $2.25.  17.  $1.60.  18.  900  bu.  19.  $216.  20.  $987. 
21.  $99.75.  22.  $120.96.  23.  $230.88.  24.  $486.08.  25.  $113.52. 
26.  $103.68.  27.  $145.26.  28.  $346.64.  29.  $588.90.  30.  $1404. 
31.    $210.24.     32.   $921.60.     33.   $10.80.     34.    $201.60.     35.  $69.04. 

Page  177.  — 1.  $1.70. 

Page  178.  — 2.  $2.94.  3.  $13.05.  4.  $  .90.  5.  $1.92.  6.  $32.26. 
7.    $23.50.     8.    $1.64.     9.   $1.90.     10.    $64. 

Page  180. —1.  2  gal.  2.  96  pk.  3.  432  sq.  in.  4.  61ft.  5.  1440  in. 
6.  800  oz.  7.  12,000  1b.  8.  18|  bu.  9.  11,250  ft.  10.  J  ft.  11.  1920  rd. 
12.  120  yd.  13.  405  ft.  14.  774  sq.  yd.  15.  11  doz.  +  11  ;  13  doz.  +  9  ; 
16  doz.  +  3.         16.    1728  sq.  in.         17.   78  sq.  ft.  18.   S  .20  profit  per  bu. 

19.    1008  sq.  ft.  in  floor  ;  1008  sq.  ft.  in  ceiling.     20.   3600  ft.     21.    $32. 

Page  181. —  1.    $16,800.    2.   $9750.     3.   .$440.    4.  $162.    5.  8400. 


298 

ANSWERS 

Page  182.— 

1.  a. 

256,  rem.  50 

;     &• 

106,  rem. 

172 

c. 

37,  rem.  537. 

2.  a. 

1237,  rem.  7 

6. 

98,  rem. 

179 

c. 

89,  rem.  764. 

3.  a. 

236,  rem.  15 

6. 

109,  rem. 

423 

c. 

158,  rem.  144. 

4.  a. 

1523,  rem.  6 

h. 

98,  rem. 

174 

;       c. 

46,  rem.  684. 

5.  a. 

355,  rem.  71 

b. 

100,  rem. 

124 

c. 

99,  rem.  454. 

6.  a. 

979,  rem.  13 , 

b. 

122,  rem. 

658 

c. 

63,  rem.  415. 

7.  a. 

1039,  rem.  25 

b. 

221,  rem. 

4 

c. 

172,  rem.  80. 

8.  a. 

2120,  rem.  22 

b. 

110,  rem. 

345 

c. 

24,  rem.  48. 

9.  a. 

2678,  rem.  11 

b. 

18,  rem. 

768, 

c. 

83,  rem.  .346. 

10.  a. 

671; 

b. 

165,  rem. 

387 

c. 

62,  rem.  222. 

11.  a. 

598,  rem.  50 

b. 

188,  rem. 

346 

c. 

215,  rem.  125. 

12.  a. 

207,  rem.  25 

b. 

109,  rem. 

202 

c. 

40,  rem.  802. 

13.  a. 

392,  rem.  28 

b. 

79,  rem. 

546 

c. 

117,  rem.  46. 

14.  a. 

2008,  rem.  9 

b. 

105,  rem. 

68 

>       c. 

252,  rem.  220 

15.  a. 

957,  rem.  6 

b. 

84,  rem. 

39 

c. 

57,  rem.  241 

16.  «. 

1044,  rem.  25 

b. 

36,  rem. 

46 

c. 

83,  rem.  364 

17.  a. 

2089,  rem.  .30 

b. 

80,  rem. 

25 

,                  c. 

113,  rem.  331 

18.  a. 

757,  rem.  46 

b. 

307,  rem. 

43 

c. 

68,  rem.  591 

19.  a. 

1279,  rem.  47 

b. 

267,  rem. 

53 

c. 

103,  rem.  196 

20.  a. 

987,  rem.  64 

b. 

58,  rem. 

174 

c. 

133,  rem.  76. 

21.  a. 

954,  rem.  13] 

b. 

42,  rem. 

388 

c. 

249,  rem.  186. 

22.  a. 

810,  rem.  17; 

b. 

77,  rem. 

237 

;      c. 

83,  rem.  18 

23.  a. 

1234,  rem.  40 

b. 

131,  rem. 

400 

c. 

154,  rem.  307. 

Page  183.  —24.  Children,  5240  ;  $  786  ;  adults,  12,641  ;  $  3160.25  ; 
one-horse  vehicles,  1-388;  $485.80  ;  two-horse  vehicles,  796,  $398  ;  total, 
$4830.05.  25.   Tiies.  $  1083.20  ;    Wed.,  $  1326.40  ;     Thurs.,    $1008.50; 

Fri.,  $1411.95.  26.   $4830.05  ;  $4830.05.  27.   $12.50.  28.    $.36. 

29.   $105.  30.    $.18.  31.  $4060.        32.  61^  lb.        33.   770  girls, 

462  boys. 


Page  184.  — 34.   58  wk.         35.   $12.16.         36.  $36.86|.  37.  $2.31. 

38.  $356.  39.   $1.50.  40.   $840.  41.  $.60.  42.  36ft.; 

5184  sq.  ft.  43.   $5.76. 


Page  185.— 44.  40  people.  45.  210  rd.  46.  30  sq.  yd.  47.  22  yd.; 
66  ft.  ;  792  in.  48.  $.46.  49.  7^  ft.  ;  468  sq.  in.  50.  $15.  51.  $11.77^. 
52.    75,273,334.     53.   $13. 


ANSWERS  299 


FIFTH  YEAR 


Page  189. -16.  6 J  in.  17.  13|  yd.  18.  2|  ft.  19.  llj  ft.  20.  9|ft. 
21.    lUyd.     22.   4  ft.    23.   46|  ft. 

Page  191.-14.  -^S^V  15.  294  mi.  16  $16^.  17.  9|.  18.  34^  mi. 
19.    $62i^V      20.   90^.      21.    321  da.      22.    $1^.      23.    12^^  hr.      24.    ^ij\. 

25.  36/j  min. 

Page  192.-10.    14|  ft.       11.    64^^^  ft.       12.   49|.      13.    30H.      14.  $4^. 
15.   oHyd.     16.   45p5mi.     17.    16^^.     18.    15|  ft.     19.    54  rd. 
Page  193. -12.    106f.      13.    43^-       14.    104||.      15.    24f.      16.   98i|  ft. 

17.  75fmi.       18.    50  bu.        19.    35f  da.        20.   2^.       21.    2j%.       22.   2j\. 
23.    2^2.     24.  2T'^in.     25.    2^|  bu.     26.   4^  lb.     27.  10|  da. 

Page  194. -9.   77^\  in.     10.  84||  bu.     11.   7H|.     12.    88i|.     13.  2^2  yd. 

14.  7TVcla.     15.    15f.     16.    3H|. 

Page  196.-2.  x^^,xV  ^.  j%  {I  ^-Ihih  5-  ^h -h-  6.  f ,  |,  |. 
7.    hhl-      8-    iVA,tV      9-    M'ifi»3^-      11-    h      12.   h      13.   I    14.    h 

15.  i.     16.    f     17.    f.      18.   |.      19.    i.    20.    f.      23.   2.     24.    i^.     25.    If. 

26.  9.     27.   4^. 

Page  199.-2.    f.     3.   |.     4.    ,V     5.    f.     6.   if.     7.   j\.     8.   yV     9.   f. 

10.  ^V      11.    A.       12.    ii.      13.    f.      14.   A.      15.     H.      16.    rV      17-    tV 

18.  f.       19.   i      20.   ^^\.      21.    l^J^yd.      22.    $^. 
2.    ]2|.     3.    28rV     4.    29f.     5.    137i. 

Page  200. -6.   58f.  7.    72^.         8.    148f         9.  3953!g.        10.   385|. 

11.  1582^.         12.   23|i         13.    140f.         14.    8f  mi.        15.    $66^. 

2.    16'-.       3.   21 9f.       4.   99.K       5.    92 H-     6.    192.       7.    1038.       8.   43,5^. 

9.  50?. 

Page  201. -10.  153.  11.  109}^.  12.  671f  13.  470^8^.  14.  I  If 
15.   $33.         16.    4|A.         17.    28f  in. 

Page  202. -2.  IJ.  3.  3J.  4.  3^\.  5.  9}.  6.  5f  7.  30,^. 
8    4jSp         9.   2f.        10.    5f         11.    4f. 

Page  203.-12.  f^.         13.   $3^.        14.  $J.       15.  9^  in.       16.  13^^  A. 

2.  f         3.    ^V-      4.  tV-      5-  f.        6.  /x-        7.  ^V-        8-    tV  «•  A- 

10.  ^V-          11    ^^-          12.  |.         13.   3j3^.         14.    ^V        16.  ^5.  16.    i. 
17.    i.    18.    ^V.         19.  1^3^-         20.   ^V        21.    ^^.        22.    ^V 

Page  204.  -  23.  |  yd.  24.  ^V  A.     25.  ^^  of  the  distance.    27.  2f    28.  llf 

29.    17f          30.   81.  31.   2f.          32.   99iV.           33.    17 ^V           34.   21t^. 

35.    6|.          36.   27t\.  37.  54^^.          38.    ^^jj.          39.    124^|.         40.  9f 

41.    132f          42.  43||.  43.   lOJ.         44.   39f.          46.  6^^.        46.   SOjV 

47.   47f        48.    i^lf  49.    7^  gal.        50.    9|  bu. 


300  ANSWERS 

Page  205.  — 52.*  1  J.  53.  3i.  54.  7i.  55.  8i.  56.  7|.  57.  13 jV 
58.  la^L-  59-  53t6-  60.  622V  61.  55^^  62.  66f  63.  66f.  64.  ld^\. 
66.  13^5.  66.  4S^\.  67.  43^^.  68.  10 1?^.  69.  12/^.  70.  40 j%.  71.  7|. 
12.  12f  A.  73.  2/5  hr.  74.  .$7^.  75.  ^^  mi. 

1.  $lf  2.  5ift.  3.  $2^^. 

Page  206.— 4.  $2|f.   5.  1ft.   6.  7|  ft.   7.  8J  T.    8.  12^V '«• 

6.  8igal.   10.  S24^||.   11.  291  mi.   12.  45f.   13.  8xV   14.  aiDj?^. 

15.  8^  mi.  16.  .$30if. 

Page  207.  — 17.  ^S^^^.  18.  $29^^.     19.  .|21ii.  20.  43^%  hr. ;  28fi- hr. 

Page  209.  — 1.  $900.  2.  1000  A.;  1000  A.;  500  A. 

Page  210.  — 3.  292 da.  4.  $160.  5.  $5460.  6.  9200 girls; 
5520  boys.  7.  $35.  8.  $648.  9.  $5800. 

Page  211.  — 1.  27  pupils.  2.  $24.  3.  30  words.  4.  49  lambs. 
5.  180  da.  6.  $120.  7.  $600.  8.  $225.  9.  66  mi.  10.  $5060. 

Page  212.  — 11.  442  mi.  12.  72  ft. 

Page  213.  — 2.  36.  3.  45.  4.  24.  5.  45.  6.  36.  7.  32.  8.  102, 
9.  51.   10.  18.    11.  24.   12.  45.   13.  108.   14.  575.    15.  2685. 

16.  1826.    17.  640.    18.  1320.    19.  360.    20.  2325.    21.  1768. 
22.  1470.   23.  720.  24.  1760.  25.  376.   26.  1425.   27.  825.   28.  3030. 

Page  214.  — 29.  $150.  30.  $525.  31.  $.3.75  cost;  $2.25  gain. 
32.  $2.80.  33.  $.50.  34.  $2.30.  35.  $3.  36.  500  mi.  37.  $845. 
38.  99  cd.  39.  $257.25.  40.  $679. 

Page  215.  — 41.  $15,000.  42.  $5680.  43.  $1.35.  44.  2681  rd. 
45.  74011  mi.  46.  1409^^  T. 

Page  217.— 3.  45.  4.  138.  5.  326.  6.  4806.  7.  10,806.  8.  1100. 
9.  3927.  10.  6006.  11.  4284.  12.  1704.  13.  9729.  14.  15,606. 
15.  9004.  16.  3241.  17.  2005.  18.  2315.  19.  2499.  20.  3027. 
21.  8165.  22.  14,885.  23.  114.  24.  144.  25.  249.  26.  64-5.  27.  3996. 
28.  2012.  29.  14,895.  30.  2092.  31.  6276.  32.  5615.  33.  2476. 
34.  4900.  35.  470.  36.  208.  37.  7990.  38.  4104.  39.  348.  40.  1020. 
41.  5971.  42.  196.  43.  357.  44.  1687.  45.  438  mi.  46.  $73.50. 
47.  $24.75.  48.  $220. 

Page  218.  — 49.  $1.86.  50.  $1.74.  51.  $94.  52.  $138.  53.  $201. 
54.  660  mi.  55.  $4809.  56.  $78f. 

Page  219.-2.  ff.  3.  ||.  4.  H-  »•  H-  6.  |§.  7.  ff  8.  if. 
9.  If.  10.  fe.  11.  ^V  12.  if.  13.  U'  15.  4i.  16.  8|.  17.  4|. 
18.  10^.  19.  21^.  20.  5|.  21.  33^^-  22.  1205.  23.  60i|.  24.  52|. 
25.  33 J.  26.  156^.  27.  261^.  28.  159f^.  29.  142|^. 

1.  $2.  2.  $2.97. 

Page220.  —  3.    $6.03.  4.    $138^.  5.    $141f.  6.    $3.76. 

7.  $8.16.  8.    $4.02.  9.   $38.06.  10.    $3.50.  11.    $301|. 
12.   $38.26^.        13.   $10,811.        14.   663^  lb.        15.    142  mi.        16.    147  mi. 


ANSWERS  301 

Page  221.— 2.  2S.  3.  9|.  4.  12.  6.  10|.  6.  IJ.  7.  7U. 
8  106.  9.  49.  10.  3^.  11.  85.  12.  33f.  13.  37i.  14.  54. 
1&.    iW*^.  16.   $5|.  17.   $144.  18.   364|mi.        "    19.   |34§. 

20.  ^%>^. 

Page  224.— 2.  18.         3.   5f.          4.   10.        5.    3|.         6.    4^.  7.    16 

8.    2.          9.    40.  10.    12.         11.  3|.          12.    1\.          13.    2^.  14.    2 

15.  2}^.     16.   9.  17.    4.       18.    7 J.     19.    3i.     20.    $.16.     21.   $5.  22.    30. 

23.  $.12. 

Page  i25.^2.    3.      3.   4.      4.   3.      5.   4.     6.    6^.     7.   li.     8.    2.     9.    5. 

10.    liV     11.    Iff.     12.    11.     13,    If.     14.    \.     15.    ItV     16.    If     17.    2^f. 

18.  11.      19.    l|f      20.    16  vests.     21.   7  pictures.     22.   24  yd.     23.    16  gal. 

24.  12  hatri.         25.    12  lamps.  26.    ^-f.  27.  3.         28.    7. 

Page  227.-2.  27.  3.  40.  4.  36.  5.  49.  6.  40.  7.  77. 
8.    63.     9.    72.     10.    81.      11.    100.      12.    96.     13.    117.     14.    144.     15.    108. 

16.  60.       17.   225.       18.    171.       19.    910.       20.    204.       21.    405.      22.    504. 

23.  10.  24.  12.  25.  9.  26.  10.  27.  16.  28.  16.  29.  9.  30.  20. 
31.  27.  32.  24.  33.  40.  34.  45.  35.  42.  36.  100.  37.  40.  38.  45. 
39.  204.  40.  63.  41.  80.  42.  3f.  43.  3|.  44.  4|.  45.  3f  46.  4^. 
47.  3^.       48.   4f       49.    5f.       50.   2\. 

Page  228.^1.  1^  2.  2.  3.  2\.  4.  \\.  5.  \^^.  6.  152|.  7.  ||. 
8.    2\.     9.    3^.     10.    4f     11.    12|.       12.    If.      13.    \\\.     14.    2^^.     15.    3^. 

16.  f.      17.    li-      18.    2^V      19.   ^.      20.    121.      21.    7.     22.    ^^i^.     23.    |f. 

24.  43yV.  2a.  42|.  26.  8y%.  27.  13|.  28.  i\.  29.  2||.  30.  ^V 
31.    $205.03xV.     32.    $631f     33.    $2105f.     34.   126  badges. 

Page  229.^^35.    $11,340.       36.    70.         37.    $1.35.         39.    |.        40.   \\. 

41.   50  ft.  42.   $60.  43.   20^  rd.         44.   25f|  mi.         46.    434»V  lb. 

46.    2112  steps.  47.   929 [f  lb. 

Page  232.-1.  $18^V-      2.    $12|.      3.    17 J  yd.      4.   $40.50.       5.    9  yd. 

6.  157  1b.  •:.  $4125.  8.  46  da.  9.  $370,  son;  $  1480,  daughter; 
$  1665,  widow;  $  925,  hospital.          10.    81^  yd.  11.    100^  hr. 

Page  233.  — 12.    $4128.       13.   16.       14.   450.      15.   $3.31^.       16.    $24. 

17.  $54.  18.  79  families.  19.  $11.60.  20.  $3.90.  21.  25^. 
22.    $.18.          23.    31 J;^.          24.    $35.95. 

Page  234.— 25.  $5.  26.  8^  yd.  27.  12.  28.  15  mi.  29.  75i  A. 
30.  8124.  31.  48  books.  32.  $38.  33.  $38^.  34.  $49.  35.  50  chairs. 
36.  4|yd.      •  37.    14^  yd.        38.    $5.25.         39.   232  pencils. 

Page235.  — 40.  15  coats.  41.  105f  lb.  42.  57f  bu.  43.312  yd. 
44.  25^  da.  45.  106f  bu.  46.  $.20.  47.  $81.  48.  $800.  49.  $.55. 
50.   220  sheep.         62.   33  bu.         53.    35^;2^^;6|.         54.    $.20. 

Page  240.-2.   ^V     3.    f^    4^   ^^.    5.   if    6.   f.     7.    ^V-     8-   i-  9-    \l 

12.    .25;  .75;  .125;  .375.      13.  ^V       14.   f.     15.   f.     16.   ^f.     17.    |.  18.   |. 

19.  1.  20.  |.  21.  i.  22.  jV  23.  ff.  24.  if.  25.  f  26.  i?.  27.  ^V 
28.  h     29.  ^L.     30.    ^2^.     31.    ^-^.     32.   ^V     33.   ^\.     34.   ^%.     35.  ^V-  36.    f. 

Page  241.—    2.   1.015.  3.   .221.         4.   .256.        5.   9.1.        6.    13.189. 

7.  .0311.         8.    18.027.         9.   .0922. 


302  ANSWERS 

• 

Page  242.-10.  44.85.      11.2.9.      12.17.165.      13.38.793.  14.26.676. 

15.   14.806.         16.  143.192.         17.  137.768.         18.  2171.812.  19.  225.303. 

20.  47.97.          21.  2.75  bu.          22.  $4.94.          23.  82.1  mi.  24.  5.25  1b. 

25.  23.93  mi. 

Page  243.-2.  5.79.        3.  12.954.  4.  .305.       5.  180.892.        6.  16.02. 

7.  72.927.     8.  695.725.      9.  18.835.     10.   131.745.     11.  38.615.      12.  32.996. 

13.  108.967.         14.  $3.75.  15.  5.375  mi.         16.  55.75  A.         17.  •'$2.20. 

Page  244.-18.  10.86  ft.  19.  28.46  ft.  20.  $2.05.  21.  6.75  1b. 

22.  5.125  1b.    23.   .375  1b.    24.  27.6  T.    25.  6.75  yd.    26.  $6.32.    27.  $4.35. 

Page  245. -2.  .12.       3.  .045.        4.  1.36.       5.  2.277.        6.  6.79.        7.  .3. 

8.  3.024.         9.   .486.        10.  74.046.        11.  2.738.        12.  61.64.        13.  31.02. 

14.  3.63.         15.  18.213.         16.  4.56.         17.  2.916. 

Page  246.-18.  $5.74.  19.  $  8.40.  20.148.5  ft.  21.  $94.90. 

22.  !$  14.49.        23.  248.5  mi. 

Note.  In  business  problems  count  5  mills  or  more  as  an  additional 
cent. 

Page  247.-2.  .216.  3.  .225.  4.  .0384.  5.65.  6.5.3.58.  7.14.445. 
8.  57.92.     9.  .462.      10.  .0855.      11.   .812.      12.  6.960.      13.  1710.      14.  3.1. 

15.  90.9.  16.  .468.  17.  7.92.  18.  153.6.  19.  58.52.  20.  $1.44.  21.  $.72. 
22.   $51.56.  23.  481.95  mi.  24.  17.0625  mi.  25.  $8.97;  $15.53. 

26.  $65.         27.  796.8751b. 

Page  248. -2.  .11.       3.  .32.        4.  .101.         5.  .102.      6.  .107.       7.  .212. 

8.  .121.  9.  .156.  10.  .112.  13.  .075.  14.  .075.  15.  .045.  16.  .056. 
17.  .3.     18.  .3.     19.  .02.     20.  .001.     21.  .002.     22.  .03.     23.  .05.      24.  .03. 

25.  .004.  26.  .034.  27.  .003.  28.  .012.  29.  .005.  30.  .009.  31.  .113. 
32.  .072.  33.  .036.  34.  .04.  35.  .025.  36.  .04.  37.  .05.  38.  .007. 
39.  .011.       40.  .006. 

Page  249.-6.  3.04.       7.  2.11.       8.  6.1.       9.  22..3.  10.  .101.  11.  3.4. 

12.  .039.      13.  .124.      14.  .027.      15.   1.16.      16.   .022.  17.   .036.  18.  .14. 

19.  .0017.      20.  .029.      21.  .038.     22.  .143.      23.  6.14.  24.  6.04.  25.  .089. 

26.  .475.       27.  .605.       28.  .065.       29.  .0904. 

Page  250. -31.  .266+.  32.  .4.  33.  .105+.  34.  .08.  35.  .444+.  36.  .5. 
37.  .2.     38.  .5.     39.  .5.    40.  .25.     41.  .125.    42.  .0124+. 

Page  251.-2.  .65.     3.  .84.      4.  8.7.       5.  .74.      6.  7.4.      7.  8.5.  8.  7.7. 

9.  8.4.  10.  8.2.  11.  9.4,  12.  .87.  13.  .75.  14.  49.  15.  *89.  16.  8.4. 
17.  .83.  18.  9.5.  19.  760.  20.  .05.  21.  45.  22.  8.6.  23.  9.6.  24.  2.8. 
25.  870.     26.  670.     27.  9.2.     28.  32.1. 

Page  252.-29.  .001.  30.12.5.  31.1.^1.  32.144.  33.50.6.  34.233. 
35.  3.6.  36.  17.4.  37.  27.9.  38.  266.9.  39.  32.6.  40.  42.4.  41.  37.5. 
42.    82.3.     43.    56.1.     44.   28.3.     45.    43.6.    46.    38.4. 

1.  5.  2.  48.3.9577.  3.  $1.05.  4.  365  da.  5.  4.25  T.  6.  19.2  A. 
7.    85.375  T.     8.    29.    9.   $140.63. 

Page  253.-10.  2240.8  mi.  11.  $1.69.  12.  142  pieces.  13.  1.376  carats. 
14.   16.625  1b.       15.    1.5  T.      16.   6  qt.     17.   $20.     18.354  ft.     19.   $133.09. 

20.  220  bbl.     21.   1000. 


ANSWERS  303 

Page  256.  — 2.   8106.65.    3.    .^66.92.    4.    $126.48.     5.   $3.44.     6.   $4.54. 

7.  a31.71.     8.  $8.20.     9.  $200.40.     10.  $10.03.     11.  $35.04.     12.   $453.75. 

13.  $741.85.  14.  $3035.25.  15.  $724.  16.  $6867.84.  17.  $157.50. 
18.   $33.     19.   594  mi.    20.  $1027.     21.    $50. 

Page  257.  —  22.  403.2  rd.  23.  $386.90.  24.  $140.  25.  1  ;  2  ;  2.5  ;  3 ;  4. 
26.  $7.20.  27.  $0.  28.  $10.  29.  $128.  30.  225  sheep.  31.  24  words. 
33.   $616.     34.   $5075. 

Page  259.  — 2.   $10.     3.    $144.    4.    $27.     5.   $112.     6.    $9.     7.  $15.36. 

8.  $lt).25.     9.    $33.75.     10.   $28.50.     11.   $56.     12.   $42.75.     13.   $180.95. 

14.  $29.25.  15.  $15.75.  16.  $6;  $206.  17.  $8;  $408.  18.  $19.50; 
$169.50.  19.  $9.30;  $629.30.  -20.  $10.80;  $280.80.  21.  $16.75; 
$365.75.         22.   $287.50. 

Page  261.— 2.  $1.50.  3.  $3.75.  4.  $1.13.  5.  $.92.  6.  $28.13. 
7.  $121.50.     8.    $13.30.    9.   $6.38.     11.    46  pairs.     12.    116|  bu. 

Page  262.— 13.  4  doz.  14.  $90.  15.  $16.50.  16.  $40.55.  17.  $3.60. 
18.   25  yd. 

Page  263.  — 1.  $3.25.    2.    $173.     3.  $3.0.3.    4.    $10.45.     5.   $6.56. 

Page  264.— 6.   $4.65.     7.   $3.98.     8.    $31.09.     9.    $21.17. 

Page  265. —1.  $7.     2.    $10.95.    3.    $84.62. 

Page  267.-2.  49  pt.  3.  67  pt.  4.  38  pt.  5.  45  pt.  6.  7  pt. 
7.  $2.80.  8.  $4.  10.  187  qt.  1  pt.  11.  423  qt.  12.  34  gal.  3  qt. 
13.    84  gal.  1  qt.  1  pt.  14.    117  gal.  1  qt.  15.    1750  pt.  16.    52  qt. 

17.   1152  pt. 

Page  268.  — 1.  236  pt.  2.  H  bu.  3.  37^  bu.  4.  16i  bu.  5.  561  pt. 
6.   23^5  bu. 

Page  270.  — 1.    101  oz.  2.    6800  1b.  3.    6448  oz.  4.   8800  oz. 

6.  36  cwt.     6.  64,080  oz.      7.    34  lb.      8.   3  T.      9.    8  lb.      10.   50  lb.  10  oz. 

Page  271.- 1.    11,160  sec.        2.   l|da.        3.    7380  min.        4.  3240  da. 

5.  2160  hr.      6.   2  wk.      7.   4  da.      8.   2,592,000  sec.      9.   19,800  sec. 

Page272.  — 10.   $21.        11.  $10.80.        12.  $58.50.        13.  $21. 

Page  273.  — 1.   396  in.  2.    36  ft.  3.   154  yd.  4.  31,680  in. 

6.  138  in.       6.    76  ft.       7.   48  yd.       8.    1  rd. 

Page  274.— 1.  4320  turns.  2.  $10.08.  3.  88  rd.  4.  108  1b.;  91b. 
5.  1  gal.  1  qt.  1  pt.  6.  $145.20.  7.  9^^  lb.  8.  $63.  9.  34  doz. 
10.    1211b.        11.    1000  baskets.         12.   $25. 

Page  275.  — 13.  $3.02  change.  14.  $6.20.  15.  $21.  16.  208  cans. 
17.    $3^;  $.06|.  18.   $5.75.  19.   791b.         20.    $3.78.        21.    70  yr. 

22.    12  T.  41  lb. 


30^  ANSWERS 

Page  277. —1.  120  sq.  in.  2.  26f  sq.ft.  3.  3650  sq.  ft.  4.  36i 
sq.  in.  8.  824.  9.  ^42.63.  10.  6|  sq.  ft.  11.  |2.99.  12.  Second 
is  110  sq.  in.  larger.         13.   ^37.50. 

Page  278.  — 14.    $76.50.      15.   $192.50.       16.  :J  of  it.       17.   ^  as  large. 

Page280.  — 4.    19,200  cu.  ft.        5.   711^  cu.  yd.         6.    12  cu.  ft. 

Page  281.— 7.  384  cubes.  8.  40  sq.  ft.  9.  27,648  cu.  in.  10.  480 
cu.  ft.       11.    385.7106+  bu.       12.   6000  Ibi       13.   320  cu.  ft.       15.    18  sq.  ft. 

Page  282.  — 19.  1728  cu.  in.  21.  18  cu.  ft.  22.  27  cu.  in.  23.  64 
cu.  in.  24.    8  cu.  in.         25.    8  times.         26.    24  cu.  in.         27.   4  sq.  in. 

28.  25  more.        29.    $26.07.        30.    l3|  loads  ;  $4.17. 

Page  283.— 1.  |2.08.  2.  $6.27.  3.  102,700.  4.  $135.  5.  12^. 
6.  $.18.  7.  6  aprons.  8.  Four  thousand  six  and  fifteen  thousandths. 
9.   75  A.        10.   $240.         11.    101  pt.        12.    35  mi.        13.    37|  yd. 

Page  284.  — 14.    755,040  ft.  15.    24.  16.  $  14,400.  17.    $57. 

18.    $12.00.        19.    15  bu.  2  pk.  2  qt.       20.    $41.25.       22.    $3.75.        23.  if  ; 
^1;  ^f.  24.   21^.  26.  312  yd.  27.    ^  A.  ;  .05  A.  28.    42  1b. 

29.  $60.12.         30"   900  cu.  ft. 

Page  285.— 31.   $8.64.  32.    (1)  51.2  yd.  ;  53.76  yd. ;  42  yd.  ;  (2)  72 

pal.;    219.6  gal.  ;    27  gal.  ;  (3)    12  bu.  ;    45  bu.  ;    58  bu.             33.   $4.53. 

34.  $4.62.          35.   $288.  36.    84  1b.          37.    $28.80.          38.    $379.17. 

39.    195  yd.        40.   $1664.  41.   92f  lb. 

Page  286.— 42.  $3.99.  43.  $3798.44.  44.  100  bu.  46.  204  yd. 
46.  $600.  47.  $1.50.  48.  $1.60.  49.  $42.  50.  7  yd.  61.  $67.50. 
62.    $  224^.         53.    82  A.         54.    13|  T.         55.    74|  ft. 

Page  287.  — 56.  $  H.  67.  Mary,  $i^.  58.  $llf.  59.  4.  60.  $486.10. 
61.  70  pk.  62.  1000.  63.  72.  64.  103  pk.  65.  $17.40.  66.  4  times ; 
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73.    80  marbles.  74.    32  marbles.  75.    $7.50.  76.   143  bu.  3  pk. 

77.    $3.73.        78.   $215.25.        79.   96  loads.        80.    112.752.        81.    $29.40. 


H  IC  KS'S      C  HAM  PI  ON 
SPELLING      BOOK 

By    WARREN    E.     HICKS,    Assistant    Superintendent    of 
Schools,    Cleveland,    Ohio 

Complete,  $0.25    -    Part  One,  $0.18   -    Part  Two,  $0.18 


THIS  book  embodies  the  method  that  enabled  the  pupils 
in  the  Cleveland  schools  after  two  years  to  win  the  Na- 
tional Education  Association  Spelling  Contest  of  1908. 
^  By  this  method  a  spelling  lesson  of  ten  words  is  given  each 
day  from  the  spoken  vocabulary  of  the  pupil.  Of  these  ten 
words  two  are  selected  for  intensive  study,  and  in  the  spelling 
book  are  made  prominent  in  both  position  and  type  at  the  head 
of  each  day's  lessons,  these  two  words  being  followed  by  the 
remaining  eight  words  in  smaller  type.  Systematic  review  is 
provided  throughout  the  book.  Each  of  the  ten  prominent 
words  taught  intensively  in  a  week  is  listed  as  a  subordinate 
word  in  the»next  two  weeks;  included  in  a  written  spelling 
contest  at  the  end  of  eight  weeks ;  again  in  the  annual  contest 
at  the  end  of  the  year ;  and  again  as  a  subordinate  word  in  the 
following  year's  work; — used  five  times  in  all  within  two 
years. 

^  The  Champion  Spelling  Book  consists  of  a  series  of  lessons 
arranged  as  above  for  six  school  years,  from  the  third  to  the 
eighth,  inclusive.  It  presents  about  1,200  words  each  year, 
and  teaches  3  i  2  of  them  wdth  especial  clearness  and  intensity. 
It  also  includes  occasional  supplementary  exercises  which  serve 
as  aids  in  teaching  sounds,  vowels,  homonyms,  rules  of  spell- 
ing, abbreviated  forms,  suffixes,  prefixes,  the  use  of  hyphens, 
plurals,  dictation  work,  and  word  building.  The  words  have 
been  selected  from  lists,  supplied  by  grade  teachers  of  Cleve- 
land schools,  of  words  ordinarily  misspelled  by  the  pupils  of 
their  respective  grades. 


AMERICAN     BOOK     COMPANY 


STEPS   IN    ENGLISH 

By  A.  C.  McLEAN,  A.M.,  Principal  of  Luckey  School, 
Pittsburg;  THOMAS  C.  BLAISDELL,  A.M.,  Pro- 
fessor of  English,  Fifth  Avenue  Normal  High  School, 
Pittsburg;  and  JOHN  MORROW,  Superintendent  of 
Schools,  Allegheny,  Pa. 


Book  One.      For  third,  fourth,  and  fifth  years ^0.40 

Book  Two.    For  sixth,  seventh,  and  eighth  years 60 


THIS  series  presents  a  riew  method  of  teaching  language 
which  is  in  marked  contrast  with  the  antiquated  systems 
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press his  thoughts  in  language  rather  than  furnish  an  undue 
amount  of  grammar  and  rules. 

^  From  the  start  the  attempt  has  been  made  to  base  the  work 
on  subjects  in  which  the  child  is  genuinely  interested.  Lessons 
in  writing  language  are  employed  simultaneously  with  those  in 
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The  lessons  are  of  a  proper  length,  well  arranged,  and  well 
graded.  The  books  mark  out  the  daily  work  for  the  teacher 
in  a  clearly  defined  manner  by  telling  him  what  to  do,  and 
when  to  do  it.  Many  unique  mechanical  devices,  e.  g.,  a 
labor-saving  method  of  correcting  papers,  a  graphic  system  of 
diagramming,  etc.,  form  a  valuable  feature  of  the  work. 
^  These  books  are  unlike  any  other  series  now  on  the 
market.  They  do  not  shoot  over  the  heads  of  the  pupils, 
nor  do  they  show  a  marked  effort  in  writing  down  to 
the  supposed  level  of  young  minds.  They  do  not  contain 
too  much  technical  grammar,  nor  are  they  filled  with  what 
is  sentimental  and  meaningless.  No  exaggerated  attention  is 
given  to  analyzing  by  diagramming,  and  to  exceptions  to  ordi- 
nary rules,  which  have  proved  so  unsatisfactory. 


AMERICAN     BOOK     COMPANY 
C81) 


RODDY'S     GEOGRAPHIES 

By  JUSTIN   RODDY,  M.S.,  Department  of  Geography, 
First  Pennsylvania  State  Normal  School,  Millersville,  Pa. 


Elementary  Geography     .  ^0.50 


Complete  Geography   .     .  j^l.oo 


THIS  "information**  series  meets  a  distinct  demand  for 
new  geographies  which  are  thoroughly  up  to  date,  and 
adapted  for  general  use,  rather  than  for  a  particular  use 
in  a  highly  specialized  and  organized  ideal  system.  While 
not  too  technical  and  scientific,  it  includes  sufficient  physio- 
graphic information  for  the  needs  of  most  teachers. 
^  An  adequate  amount  of  material  is  included  in  each  book 
to  meet  the  requirements  of  those  grades  for  which  it  is  designed. 
This  matter  is  presented  so  simply  that  the  pupil  can  readily 
understand  it,  and  so  logically  that  it  can  easily  be  taught  by 
the  average  teacher. 

^  The  simplicity  of  the  older  methods  of  teaching  this  subject 
is  combined  with  just  so  much  of  the  modern  scientific  methods 
of  presentation  as  is  thoroughly  adapted  to  elementary  grades. 
Only  enough  physiography  is  included  to  develop  the  funda- 
mental relations  of  geography,  and  to  animate  and  freshen  the 
study,  without  overloading  it  in  this  direction. 
^  The  physical  maps  of  the  grand  divisions  are  drawn  to  the 
same  scale,  thus  enabling  the  pupil  to  form  correct  concepts 
of  the  relative  size  of  countries.  The  political  and  more  de- 
tailed maps  are  not  mere  skeletons,  giving  only  the  names 
which  are  required  by  the  text,  but  are  full  enough  to  serve 
all  ordinary  purposes  for  reference.  In  addition,  they  show 
the  principal  railroads  and  canals,  the  head  of  navigation  on 
all  important  rivers,  and  the  standard  divisions  of  time. 
^  The  illustrations  are  new  and  fresh,  reproduced  mostly 
from  photographs  collected  from  all  parts  of  the  world. 
Formal  map  studies  or  questions  accompany  each  map,  direct- 
ing attention  to  the  most  important  features. 


AMERICAN    BOOK     COMPANY     ' 

Clio) 


BROOKS'S    READERS 

By    STRATTON    D.    BROOKS,   Superintendent 
of  Schools,  Boston,  Mass. 


FIVE  BOOK  SERIES 

First  Year $0.25 

Second  Year 35 

Third  Year 40 

Fourth  and  Fifth  Years    .        .50 
Sixth,   Seventh,   and 

Eigjith  Years     .     .     .        .60 


EIGHT    BOOK   SERIES 

First  Year i^o.25 

Second  Year      .    *.     ,      .        .35 

Third  Year 40 

Fourth  Year 40 

Fifth  Year 40 

Sixth  Year 40 

Seventh  Year 40 

Eighth  Year 40 


THESE  readers  form  a  good  all-round  basal  series,  suit- 
able for  use  in  any  school ;  but  they  will  appeal  to 
teachers  particularly,  because  of  their  very  easy  gradation. 
Both  in  thought  and  expression,  the  books  are  so  carefully 
graded  that  each  selection  is  but  slightly  more  difficult  than 
the  preceding  one,  and  there  is  no  real  gap  anywhere. 
^  Although  a  wide  variety  of  reading  matter  is  provided, 
good  literature,  embodying  child  interests,  has  been  considered 
of  fundamental  importance.  Lessons  of  a  similar  nature  are 
grouped  together,  and  topics  relating  to  kindred  subjects  recur 
somewhat  regularly.  All  are  designed  to  quicken  the  child's 
observation,  and  increase  his  appreciation. 
^  By  the  use  of  this  series,  the  child  will  be  taught  to  read  in 
such  a  manner  as  will  appeal  to  his  interests,  and  at  the  same  time 
he  will  be  made  acquainted  with  the  masterpieces  of  many  fa- 
mous writers.  He  will  gain  a  knowledge  of  many  subjects,  and 
acquire  pure  and  attractive  ideals  of  life  and  conduct.  His  imagi- 
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also  be  taught  a  love  of  country,  and  given  glimpses  into  the 
life  of  other  lands. 

^  The  books  are  very  attractive  in  mechanical  appearance, 
and  contain  a  large  number  of  original  illustrations,  besides 
reproductions  of  many  celebrated  paintings. 


AMERICAN     BOOK     COMPANY 


•liO 


CARPENTER'S    READERS 

By  FRANK  G.    CARPENTER 
GEOGRAPHICAL     READERS 


North   America  .  .  ^0.60 

South  America  .  ,  .60 

Europe  .           .  .  .  .70 

As:a        .           .  .  .  .60 


Africa    ....   j55o.6o 
Australia,   Our  Colonies, 
and  Other  Islands  of  the 
Sea     .  .  .  .        .60 


READERS  ON  COMMERCE  AND  INDUSTRY 
How  the  "World  is  Fed       .   $0.60     I     How  the  World  is  Clothed    $0.60 


CARPENTER'S  Geographical  Readers  supplement  the 
regular  text-books  on  the  subject,  giving  life  and  interest 
to  the  study.  They  are  intensely  absorbing,  being 
written  by  the  author  on  the  spots  described,  and  presenting 
an  accurate  pen-picture  of  places  and  peoples.  The  style  is 
simple  and  easy,  and  throughout  each  volume  there  runs  a 
strong  personal  note  which  makes  the  reader  feel  that  he  is 
actually  seeing  everything  with  his  own  eyes. 
\\  The  books  give  a  good  idea  of  the  various  peoples,  their 
strange  customs  and  ways  of  living,  and  to  some  extent  of  their 
economic  condition.  At  the  same  time,  there  is  included  a 
graphic  description  of  the  curious  animals,  rare  birds,  wonder- 
ful physical  features,  natural  resources,  and  great  industries  of 
each  country.  The  illustrations  for  the  most  part  are  repro- 
ductions of  photographs  taken  by  the  author.  The  maps  show 
the  route  taken  over  each  continent. 

^  The  Readers  on  Commerce  and  Industry  give  a  personal 
and  living  knowledge  of  the  great  world  of  commerce  and 
industry.  The  children  visit  the  great  food  centers  and  see 
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prepared  for  use,  and  they  travel  in  the  same  way  over  the 
globe  investigating  the  sources  of  their  clothing.  The  journeys 
are  along  geographical  lines,  and  while  studying  the  industries 
the  children  are  learning  about  localities,  trade  routes,  and  the 
other  features  of  transportation  and  commerce. 


AMERICAN     BOOK     COMPANY 

_ 


WEBSTER'S 
SCHOOL     DICTIONARIES 

Revised  Editions 


T 


HESE  Dictionaries  have  been  thoroughly  revised, 
entirely  reset,  and  made  to  conform  to  that  great  stand- 
ard authority — Webster's  International  Dictionary. 


WEBSTER'S  PRIMARY  SCHOOL  DICTION- 
ARY   ^0.48 

Containing  over  20,000  words  and  meanings,  with  over 
400  illustrations. 

WEBSTER'S  COMMON  SCHOOL  DICTION- 
ARY   ^0.72 

Containing  over  25,000  words  and  meanings,  with  over 
500  illustrations. 

WEBSTER'S  HIGH  SCHOOL  DICTIONARY,  $0.98 

Containing  about  37,000  words  and  definitions,  and  an 
appendix  giving  a  pronouncing  vocabulary  of  Biblical, 
Classical,  Mythological,  Historical,  and  Geographical  proper 
names,  with  over  800  illustrations 

WEBSTER'S  ACADEMIC  DICTIONARY 

Cloth,  ^1.50;  Indexed ;^i.8o 

Half  Calf,  ;^ 2.75  ;  Indexed 3.00 

Abridged  directly  from  the  International  Dictionary,  and 
giving  the  orthography,  pronunciations,  definitions,  and 
synonyms  of  about  60,000  words  in  common  use,  with  an 
appendix  containing  various  useful  tables,  with  over  800 
illustrations. 

SPECIAL  EDITIONS 

Webster's  Countinghouse  Dictionary.      Sheep, 

Indexed ^2.40 

Webster's  Handy  Dictionary 15 

Webster's  Pocket  Dictionary 57 

The  same.      Roan,  Flexible      ....        .69 

The  same.      Roan,  Tucks -7^ 

The  same.      Morocco,  Indexed    ...        ^90 


AMERICAN    BOOK     COMPANY 

(104) 


UNITED  STATES  HISTORIES 

By  JOHN  BACH  McMASTER,    Professor  of  American 
History,  University  of  Pennsylvania 


Primary  History,  ^0.60       School  History',  $i.oo       Brief  History,  ^i-oo 


THESE  Standard  histories  are  remarkable  for  their 
freshness  and  vigor,  their  authoritative  statements, 
and  their  impartial  treatment.  They  give  a  well- 
proportioned  and  interesting  narrative  of  the  chief  events 
in  our  history,  and  are  not  loaded  down  with  extended 
and  unnecessary  bibliographies.  The  illustrations  are  his- 
torically authentic,  and  show,  besides  well-known  scenes 
and  incidents,  the  implements  and  dress  characteristic  of  the 
various  periods.  The  maps  are  clear  and  full,  and  well 
executed. 

^  The  PRIMARY  HISTORY  is  simply  and  interestingly 
written,  with  no  long  or  involved  sentences.  Although  brief, 
it  touches  upon  all  matters  of  real  importance  to  schools  in 
the  founding  and  building  of  our  country,  but  copies  beyond 
the  understanding  of  children  are  omitted.  The  summaries 
at  the  end  of  the  chapters,  besides  serving  to  emphasize  the 
chief  events,  are  valuable  for  review. 

^  In  the  SCHOOL  HISTORY  by  far  the  larger  part  of 
the  book  has  been  devoted  to  the  history  of  the  United  States 
since  1783.  From  the  beginning  the  attention  of  the  student 
is  directed  to  causes  and  results  rather  than  to  isolated  events. 
Special  prominence  is  given  to  the  social  and  economic 
development  of  the  country. 

«[[  In  the  BRIEF  HISTORY  nearly  one-half  the  book 
is  devoted  to  the  colonial  period.  The  text  proper,  while 
brief,  is  complete  in  itself;  and  footnotes  in  smaller  type 
permit  of  a  more  comprehensive  course  if  desired.  Short 
summaries,  and  suggestions  for  collateral  reading,  are  provided. 


AMERICAN     BOOK     COMPANY 

4"6) 


APPLIED     PHYSIOLOGIES 

By    FRANK    OVERTON,    A.M.,    M.D.,    late    House 
Surgeon  to  the  City  Hospital,   New  York  City 


Primary  Physiology  .     .     .    ^o.-30  Intermediate  Physiology     .   $0.50 

Advanced   Physiology    .      .  ^0.80 


OVERTON'S  APPLIED  PHYSIOLOGIES  form  a 
series  of  text-books  for  primary,  grammar,  and  high 
schools,  which  departs  radically  from  the  old-time 
methods  pursued  in  the  teaching  of  physiology-  These  books 
combine  the  latest  results  of  study  and  research  in  biological, 
medical,  and  chemical  science  whh  the  best  methods  of 
teaching. 

^  The  fundamental  principle  throughout  this  series  is  the 
study  of  the  cells  where  the  essential  functions  of  the  body 
are  carried  on.  Consequently,  the  study  of  anatomy  and 
physiology  is  here  made  the  study  of  the  cells  from  the  most 
elementary  structure  in  organic  life  to  their  highest  and  most 
complex  form  in  the  human  body. 

^  This  treatment  of  the  cell  principle,  and  its  development 
in  its  relation  to  life,  the  employment  of  laboratory  methods, 
the  numerous  original  and  effective  illustrations,  the  clearness  of 
the  author*  s  style,  the  wealth  of  new  physiological  facts,  and  the 
logical  arrangement  and  gradation  of  the  subject-matter,  give 
these  books  a  strength  and  individuality  peculiarly  their  own. 
^  The  effects  of  alcohol  and  other  stimulants  and  narcotics 
are  treated  in  each  book  sensibly,  and  with  sufficient  fullness. 
But  while  this  important  form  of  intemperance  is  singled  out, 
it  is  borne  in  mind  that  the  breaking  of  any  of  nature's  laws 
is  also  a  form  of  intemperance,  and  that  the  whole  study  of 
applied  physiology  is  to  encourage  a  more  healthful  and  a 
more  self-denying  mode  of  life. 

^  In  the  preparation  of  this  series  the  needs  of  the  various 
school  grades  have  been  fully  considered.  Each  book  is  well 
suited  to  the  pupils  for  whom  it  is  designed. 


AMERICAN     BOOK     COMPANY 


THE     ELEANOR     SMITH 
MUSIC    COURSE 

By  ELEANOR  SMITH,  Head  of  the  Department  of 
Music,  School  of  Education,  University  of  Chicago, 
Director  of  Hull  House  Music  School. 


First  Book 
Second  Book 


$0.25 
•30 


Third  Book    ....       $0.40 
Fourth  Book 50 


THIS  rrxusic  series,  consisting  of  four  books,  covers  the 
work  of  the  primary  and  grammar  grades.  It  contains 
nearly  a  thousand  songs  of  exceptional  charm  and 
interest,  which  are  distinguished  by  their  thoroughly  artistic 
quality  and  cosmopolitan  character.  The  folk  songs  of  many 
nations,  selections  from  the  works  of  the  most  celebrated 
masters,  numerous  contributions  from  many  eminent  Ameri- 
can composers,  now  presented  for  the  first  time,  are 
included. 

^  The  Eleanor  Smith  Music  Course  is  graded  in  sympathy 
with  the  best  pedagogical  ideas — according  to  which  every 
song  becomes  a  study,  and  every  study  becomes  a  song. 
Technical  points  are  worked  out  by  means  of  real  music, 
instead  of  manufactured  exercises;  complete  melodies,  instead 
of  musical  particles.  Each  technical  point  is  illustrated  by  a 
wealth  of  song  material.  A  great  effort  has  been  made  to 
reduce  to  the  minimum  the  number  of  songs  having  a  very 
low  alto. 

^  The  course  as  a  whole  meets  the  demands  of  modern 
education.  Modern  life  and  modern  thought  require  the 
richest  and  best  of  the  past,  combined  with  the  richest  and 
best  of  the  present,  so  organized  and  arranged  as  to  satisfy 
existing  conditions  in  the  school  and  home.  The  series 
is  world  wide  in  its  sources,  universal  in  its  adaptation, 
and  modern  in  the  broadest  and  truest  sense  of  the 
word. 


AMERICAN     BOOK     COMPANY 


(140) 


ATTRACTIVE  SONG  BOOKS 

FOR  ELEMENTARY  AND 

HIGH   SCHOOLS 


$0.50 
.65 

.70 

•  15 
.15 

•  15 
.15 
.65 


Aiken's  Music  Course.      In  one  book 

Part  Songs  for  Mixed  Voices  . 
Betz's  Gems  of  School  Song  (Complete) 

Songs  of  Home  and  Pleasure  . 

Songs  of  Nature 

Songs  of  the  Seasons 

Songs  for  Morning,  Evening,  and  Night 
Birge's  Choruses  and  Part  Songs  for  High  Schools 
Brewster  &  Thomas's  Song  Stories  and  Songs  for 

Children .60 

Franklin  Square  Song  Collection.       Nos.    i,  2,  3, 

4»  5>  6,  7,  and  8       .      .      .        Each,  .60 

Gantvoort's  High  School  Ideal .60 

Johnson's  Songs  Every  One  Should  Know     ...  .50 

Jones's  Songs  of  Seasons .25 

Loomis's  Progressive  Glee  and  Chorus  Book       .     .  .84 

MacConnell's    Standard    Songs    and    Choruses    for 

High  Schools .75 

Mathews's  Songs  of  All  Lands .50 

McCaskey's  Favorite  Songs  and  Hymns  ....  .80 

Natural  Advanced  Music  Reader 1.09 

Natural  Music  Leaflets :   Prices  from  2c.  to  8c.  each. 

Special  list  on  application. 
Neidlinger's  Earth,  Sky,  and  Air  in  Song: 

Book  I 

Book  II 

Shirley's  Part  Songs  for  Girls'  Voices 

Part  Songs  for  Mixed  Voices  . 

School  and  Festival  Songs 
Siefert's  Choice  Songs.      Book  I 

Book  II.      Revised  edition 


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SCHOOL    EDITIONS    OF 
STANDARD    FICTION 


Defoe's  Robinson  Crusoe  (Stephens)        ....      ^0.50 
Defoe's  Robinson  Crusoe.      (Adapted  for  children  by 

Baldwin) .35 

Dickens's  Story  of  Little  Nell— From  The  Old  Curi- 
osity Shop  (Gordon) 50 

Dickens's  Tale  of  Two  Cities  (Kirk) 50 

Dickens's  Twelve  Christmas  Stories  (Gordon) — A 
Christmas  Carol;  The  Child's  Story;  The 
School-boy's  Story  ;  Our  School ;  The  Seven 
Poor  Travelers ;  The  Holly-Tree  Inn  ;  A 
Christmas  Tree;  Mugby  Junction  ;  The  Ghost 
in  Master  B's  Room;  Little  Bebelle  ;  A  Child's 
Dream  of  a  Star  ;  and  The  Detective  Police  .  .50 
Dickens's  Child's  Oliver  Twist  and  David  Copper- 
field  (Severance) 40 

Lambs'  Tales  from  Shakespeare — Comedies  (Rolfe)    .      .50 
Lambs'  Tales  from  Shakespeare — Tragedies  (Rolfe)   .      .50 

Stories  from  the  Arabian  Nights  (Clarke) 60 

Scott's  Kenil worth  (Norris) 50 

Scott's  Quentin  Durward  (Norris) 50 

Scott's  Talisman  (Dewey) ojo 

Scott's  Ivanhoe 50 


THESE  masterpieces  of  English  literature  should  be 
famihar  to  every  child.  Not  only  will  they  prove  ab- 
sorbing and  interesting  in  themselves,  but  they  will  also 
create  a  love  for  good  literature,  and  awaken  in  children  a 
desire  to  read  others  of  these  authors'  works. 
^  In  their  present  editions,  the  original  narratives  have  been 
altered  only  so  much  as  was  necessary  to  make  them  compre- 
hensible to  children.  Unessential  passages  have  been  omitted, 
and  in  some  cases  the  wording  has  been  slightly  changed. 


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A    SYSTEM    OF    PEDAGOGY 

■    By  EMERSON  E.   WHITE,  A.M.,   LL.D. 


Elements  of  Pedagogy $l.oo 

School  Management  and  Moral  Training     . ,      i.oo 

Art  of  Teaching i.oo 


BY  the  safe  path  of  experience  and  in  the  light  of  modern 
psychology  the  ELEMENTS  OF  PEDAGOGY 
points  out  the  limitations  of  the  ordinary  systems  of 
school  education  and  shows  how  their  methods  may  be  har- 
monized and  coordinated.  The  fundamental  principles  of 
teaching  are  expounded  in  a  manner  which  is  both  logical 
and  convincing,  and  such  a  variety  and  wealth  of  pedagogical 
principles  are  presented  as  are  seldom  to  be  found  in  a  single 
text-book, 

^  SCHOOL  MANAGEMENT  discusses  school  govern- 
ment and  moral  training  from  the  standpoint  of  experience, 
observation,  and  study.  Avoiding  dogmatism,  the  author 
carefully  states  the  grounds  of  his  views  and  suggestions,  and 
freely  uses  the  fundamental  facts  of  mental  and  moral  science. 
So  practical  are  the  applications  of  principles,  and  so  apt  are 
the  concrete  illustrations  that  the  book  can  not  fail  to  be  of 
interest  and  profit  to  all  teachers,  whether  experienced  or 
inexperienced. 

^  In  the  ART  OF  TEACHING  the  fundamental  princi- 
ples are  presented  in  a  clear  and  helpful  manner,  and  after- 
wards applied  in  methods  of  teaching  that  are  generic  and 
comprehensive.  Great  pains  has  been  taken  to  show  the 
true  functions  of  special  methods  and  to  point  out  their  limita- 
tions, with  a  view  to  prevent  teachers  from  accepting  them 
as  general  methods  and  making  them  hobbies.  The  book 
throws  a  clear  light,  not  only  on  fundamental  methods  and 
processes,  but  also  on  oral  illustrations,  book  study,  class 
instruction  and  management,  written  examinations  and  pro- 
motions of  pupils,  and  other  problems  of  great  importance. 


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